REESE   LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 

Deceived     /^L^t/^C^i^ 

f 

^Accessions  No,  S7/  5~7<$~     Class  No.      , , 


NUMBER    WORK 


IN 


NATURE    STUDY 


PART  I. 


BY 

WILBUR  S.  JACKMAN,  A.  B., 

TEACHER  OF   NATURAL,  SCIENCE,  COOK  COUNTY  NORMAL  SCHOOL,, 

CHICAGO,  ILL,.      AUTHOR  OF  "  NATURE  STUDY  FOB 

THE  COMMON  SCHOOLS." 


CRIVEBSITI 


PUBLISHED    BY 

THE    AUTHOR 


COPYRIGHT,  1893 

BY 

WILBUR  S.  JACKMAN. 


PRESS  OP  LA  MONTE -O'DONNELL  COMPANY. 

CHICAGO. 


TO  THE    TEACHER 


The  aim  of  this  book,  briefly  stated,  is  to  show 
how  pupils  may  be  taught  to  secure,  through  mathe- 
matical processes,  definite,  accurate,  and  useful 
results  in  the  study  of  elementary  science.  The 
work  does  not  contain  arithmetical  problems,  such  as 
rnay  be  found  usually  in  the  text-books,  but  it  is  to 
be  regarded,  rather,  as  a  series  of  formulas  which  are 
to  be  applied  in  the  study  of  a  particular  subject,  as 
the  common  sense  and  judgment  of  the  teacher  may 
dictate. 

The  purpose  of  the  book  differs  so  radically  from 
that  of  the  arithmetics  used  in  the  schools,  it  becomes 
necessary  to  call  the  especial  attention  of  the  teacher 
to  the  discussion  of  the  underlying  principles,  found 
in  the  introductory  chapter,  and  to  ask  a  careful  con- 
sideration of  a  few  important  details  of  method. 

Throughout  the  work,  wherever  it  is  possible, 
individual  investigation  on  the  part  of  the  pupil  is 
presupposed;  not  an  investigation  of  the  subject  of 
number  or  of  numerical  processes,  but  of  some  phase 
of  nature  study.  It  follows,  therefore,  that  no  two 
pupils  will  work  from  exactly  the  same  set  of  data, 
though  the  relations  established  by  the  results 
obtained  should  be  and  will  be  approximately  the 
same.  Each  pupil  should  multiply  observations  and 

iii 


iv  TO  THE  TEACHER. 

collect  data  to  the  utmost  limit  of  his  time  and  abil- 
ity, that  his  final  results,  upon  which  his  conclusions 
must  rest,  may  contain,  under  the  conditions  which 
the  pupil  labored,  the  minimum  amount  of  error. 
As  a  further  check  upon  the  individual,  a  class  result, 
based  upon  an  average  of  the  results  obtained  by  all 
the  members,  may  be  required;  this  demands  the 
most  careful  management  on  the  part  of  the  teacher, 
however,  that  the  self-reliance  of  the  individual  pupil 
may  not  be  weakened  and  ultimately  destroyed. 

In  arithmetic,  as  it  is  usually  taught,  the  attention 
of  both  teacher  and  pupil  is  fixed  upon  the  process 
involved  in  the  solution  of  the  problem ;  in  this  book, 
the  attention  of  both  must  be  directed  to  the  result 
obtained  by  the  solution.  A  failure,  on  the  part  of 
the  teacher,  to  observe  this  fundamental  difference 
will  render  entirely  fruitless  any  effort  made  to  use 
this  work  effectively.  With  an  inventive  genius 
worthy  of  a  better  cause,  authors  of  text-books  in 
arithmetic  have  usually  devoted  themselves  to  devis- 
ing problems  apparently  in  the  belief  that  they 
are  interesting  and  educative  in  proportion  to  the 
labyrinthine  details  involved  in  their  solution.  Not 
one  in  a  hundred  of  such  problems  has  the  slightest 
interest  attached  to  the  result,  and  the  teacher, 
recognizing  this,  too  often  excuses  mistakes  in  calcu- 
lation, saying:  "Nevermind,  you  understand  how 
the  problem  is  done."  A  more  violent  distortion  of 
the  function  of  mathematics  in  education  can  not  be 
imagined. 

The  teacher  must  aim  to  place  a  proper  estimate 
—neither  too   high    nor  too  low — upon   the   results 


TO  THE  TEACHER.  v 

obtained.  It  may  be  impossible,  for  example,  for 
the  pupil  to  find  out,  by  any  amount  of  observation, 
measurement,  and  calculation,  the  exact  and  whole 
truth  concerning  the  relation  of  summer  and  winter 
rains  in  any  particular  region.  But,  in  the  study  of 
meteorology  and  geography,  it  is  perfectly  possible 
to  so  frame  a  series  of  problems  that  the  results  will 
indicate  a  law  and  that  each  problem  will  lead  a  step 
nearer  to  that  law.  The  measurement  of  a  dozen 
twigs  may  not  tell  much  respecting  the  relative 
growth  from  terminal  and  lateral  buds;  yet,  if  there 
be  a  law,  that  it  is,  and  what  it  is  can  be  established 
by  such  means  only,  and  it  merely  remains  for  the 
pupil  to  multiply  his  observations  that  he  may  reach 
the  truth.  It  is  ever  the  suggestion  of  law  that 
gives  intelligence  to  thought  and  this,  then,  is  to 
be  the  teacher's  guide:  first,  do  the  results  obtained 
by  a  solution  of  the  problems,  when  compared,  indi- 
cate law;  and  second,  does  a  multiplication  of  the 
problems  show  what  the  law  is?  The  questions 
are  given,  then,  with  a  definite  end  in  view  and,  if 
this  be  lost  sight  of,  they  have  absolutely  no  func- 
tion whatever. 

In  choosing  problems  to  be  solved,  the  teacher 
should  select  those  under  that  mode  of  comparison 
best  adapted  to  the  capabilities  of  the  pupils.  The 
genesis  of  the  different  modes  of  comparison  is  dis- 
cussed in  the  introductory  chapter.  The  number 
and  the  nature  of  those  to  be  solved  must  be  deter- 
mined for  each  pupil  by  the  necessities  of  the  case. 
The  sole  aim,  it  should  be  remembered,  is  to  establish 
in  the  mind  of  the  pupil  a  clear  and  definite  concept; 


vi  TO  THE  TEACHER. 

in  some  instances,  two  or  three  problems  may  suffice, 
in  others,  twice  as  many,  or,  in  some  cases,  the  entire 
list  may  be  given,  to  which  others  may  be  added. 
But  to  require  the  pupils  to  solve  an  entire  list  in 
the  usual  machine-like  arithmetic  way  could  hardly 
be  anything,  in  the  vast  majority  of  cases,  but  the 
most  arrant  nonsense.  An  effort  has  been  made  to 
give  such  a  range  and  variety  of  questions  that  the 
teacher  may  find  among  them  those  that  are  adapted 
to  the  pupils'  needs,  from  whatever  side  the  study 
of  the  subject  may  be  approached.  Each  problem 
finds  its  origin  in  the  necessities  and  the  conditions 
arising  in  the  process  of  the  development  of  intrinsic 
thought  and  it  is,  therefore,  of  fundamental  impor- 
tance that  each  result  be  clearly  interpreted. 

It  is  intended  that  the  subject  matter  found  in 
nature  study  should  furnish  whatever  illustrative 
material  may  be  necessary  in  order  to  develop  in  the 
pupil's  mind  a  correct  idea  of  the  different  arith- 
metical operations.  For  example,  it  is  not  necessary 
to  develop  the  processes  by  which  areas  and  volumes 
may  be  found  by  means  of  card-board  and  various 
solids  having  no  intrinsic  worth  to  the  pupil.  But, 
to  illustrate,  when  the  subject  of  evaporation  is  being 
studied  an  opportunity  is  then  offered  to  develop 
these  processes  by  the  very  nature  and  demand  of  the 
study  itself.  And  if  the  interest  of  the  pupils  is  gen- 
uine, if  it  is  voluntary,  not  forced,  the  mastery  of  the 
processes  involved  is  an  exceedingly  simple  matter. 

The  pupils  should  be  provided  with  every  possible 
facility  for  making  measurements  of  different  kinds 
rapidly  and  accurately.  Rulers,  balances  and 


TO  THE  TEACHER.  vii 

weights,  pencils  and  paper  should  always  be  ready 
for  instant  use.  To  avoid  delays  from  various  causes, 
a  ruler  may  be  screwed  down  to  the  top  of  each  desk 
near  one  edge,  and  with  a  pair  of  calipers  or  dividers 
measurements  may  be  made  with  great  ease.  The 
constant  presence  of  the  different  units  will  do  much 
to  fix  them  in  the  pupil's  mind.  Balances  and  suit- 
able weights  may  be  obtained  for  a  trifling  outlay, 
and  they  should  form  a  part  of  the  apparatus  of  every 
school-room.  A  brass  protractor  may  be  screwed 
against  the  wall  and  by  this  means  the  pupils  may 
learn  to  measure  angles  accurately. 

In  order  to  facilitate  the  distribution  of  work 
among  a  number  of  pupils,  it  has  been  thought 
better  to  write  out,  in  nearly  every  case,  each 
example  in  full  rather  than  to  shorten  and  combine 
several  under  one  number.  Except  where  such 
fractions  as  halves,  thirds,  fourths,  etc.,  occur,  it  is 
by  far  easier  to  use  decimals  and  this  is  strongly 
recommended.  The  ease  by  which  reductions  can  be 
made  renders  it  also  exceedingly  desirable  that  the 
metric  system  should  be  used  throughout.  For 
the  purposes  of  convenient  reference,  only,  a  list  of 
the  more  important  tables  is  given  on  another  page. 

The  problems  are  arranged  under  the  different 
months  merely  because  the  line  of  nature  study 
pursued  in  the  Cook  County  Normal  School  makes 
such  grouping  convenient.  It  is  expected  that 
teachers,  elsewhere,  will  change  the  order,  if  neces- 
sary, to  better  adapt  it  to  their  peculiar  conditions. 

W.  S.  J. 

Cook  County  Normal  School, 
Sept.  1,  1893.  Chicago,  Illinois. 


TABLE  OF  CONTENTS. 


PAGE 

To  THE  TEACHER, m-vii 

INTRODUCTION, .      ix-xxix 

METRIC  TABLES, xxx-xxxi 

SEPTEMBER, 1-72 

ZOOLOGY — Colors  of  Insects, 1-5 

BOTANY — Mutual  Relations  of  Plants  and  Animals — 

Study  of  Leaves, 6-10 

Structure  and  Colors  of  Fruits,         .        .        .  11-15 

A  Study  of  the  Constituents  of  Fruits,  .        .  16-23 

PHYSICS — Evaporation  of  Liquids,   ....  24-32 

FORM  FOR  METEOROLOGICAL  RECORD,             .     _  .  33 

METEOROLOGY, 34-42 

ASTRONOMY— Mutual  Relations  of  the  Earth  and  Sun,  43-50 

Problems, 50-54 

GEOGRAPHY — North  America— Coast  Lines  and  Relief,  55-65 

MINERALOGY— -The  Mechanicnl  Constituents  of  Soils,  66-72 

OCTOBER, 73-143 

ZOOLOGY— Study  of  Animal  Tissues,        .        .        .  73-78 

BOTANY  — Annual  Growth  of  Branches  of  Trees,     .  79-91 

The  Distribution  of  Seeds,         ....  92-99 

PHYSICS— Ebullition, 100-103 

METEOKOLOGY, 104-115 

ASTRONOMY — Variation  in  Day's  Length,  etc.,         .  116-124 

GEOGRAPHY — North  America—Drainage,        .        .  125-135 

MINERALOGY — Physical  Properties  of  Minerals,      .  136-143 

NOVEMBER, 144-198 

ZOOLOGY— Winter  Habits  of  Animals,     .        .        .  144-150 

BOTANY — Annuals,  Biennials,  and  Perennials,         .  151-155 

PHYSICS — Heat — Expansion  of  Metals,    .        .        .  156-159 

METEOROLOGY, 160-172 

METEOROLOGY — Autumn  Months  Compared,          .  173-175 

ASTRONOMY — Variation  in  Day's  Length,         .        .  176-184 

GEOGRAPHY— North  America — Zones  and' Climate,  185-198 
viii 


UN1VEB8ITT 


INTRODUCTION. 


RELATION  OF  ARITHMETIC  TO  ELE 
MENTARY  SCIENCE. 


The  introduction  of  elementary  science  into  the 
grammar  and  primary  grades  of  the  public  schools 
is  destined  to  mark  an  important  epoch  in  the  history 
of  school-teaching  in  this  country,  The  scope  of  the 
work  included  under  the  head  of  natural  science  is 
so  great  that  anything  like  a  general  introduction  of 
it  into  the  lower  grades  will  necessitate  a  thorough 
reorganization  of  the  course  as  it  has  long  existed 
and  now  stands.  The  greatest  problem  at  this  time, 
therefore,  is  one  of  readjustment,  and  it  is  not  easily 
solved;  for  the  present  course  of  study,  as  usually 
laid  down,  is  fortified  not  only  in  the  wisdom,  but 
also  in  the  prejudices  arid  traditions  of  the  past. 
The  reorganization  will  be  accomplished  partly  by  a 
displacement  of  some  of  the  studies  once  considered 
essential,  but  chiefly  by  a  readjustment  of  the  parts 
so  that  the  course  will  form  an  organic  whole. 

In  this  age  of  doubting  and  questioning,  when  the 
search-light  of  reason  is  turned  upon  every  creed 
and  custom,  the  assurance  is  that  unless  a  subject 


IX 


x  INTRODUCTION. 

can  show  a  stronger  reason  for  its  place  than  may  be 
found  in  the  homage  it  has  received  in  the  past,  it 
will  have  to  give  way.  Not  much  room  can  be 
hoped  for,  however,  in  this  direction,  for  experience 
has  shown  the  desirability  of  retaining  in  the  course 
the  greater  part,  by  far,  of  all  that  is  now  taught. 
If  any  new  subject,  therefore,  is  to  enter  the  sacred 
circle  of  the  present  curriculum,  it  must  show  itself 
capable  of  entering  into  organic  relation  with  most 
of  the  subjects  already  there. 

That  a  full  line  of  science  work  is  soon  to  be  a 
part  of  the  regular  school  programme  no  one  can 
any  longer  doubt ;  and  the  question  which  must  be 
settled,  for  the  teacher,  and  by  the  teacher,  is,  what 
relation  does  it  bear  to  the  work  already  being  done  ? 
The  basis  upon  which  the  answer  must  rest  is  found 
in  the  nature  of  mental  action.  In  mind  movement 
we  may  logically,  if  not  actually,  discern  the  thought, 
and  the  form  embodying  it  or  through  which  it  is 
expressed.  All  studies,  then,  naturally  fall  into  two 
divisions  which  may  be  distinguished  as  thought 
studies  and  form  studies.  As  it  is  difficult  to  con- 
ceive, much  more  to  define,  thought  independent  of 
the  form  through  which  it  is  expressed,  so  it  is  diffi- 
cult, if  not  impossible,  to  exactly  define  and  precisely 
distinguish  thought  studies  from  form  studies.  Log- 
ically, such  a  distinction  does  exist;  actually,  how- 
ever, in  ideal  educational  methods  it  does  not.  How 
far  we  are  and  have  been  from  such  an  ideal,  the 
present  bootless  pursuit  of  pure  form  work  will  tes- 
tify. Form  studies  have  always  been  held  to  be  of 
great  value  as  a  means  of  discipline ;  thought  studies 


INTRODUCTION.  xi 

MIV  those  which  deal  with  knowledge  that  is  in  itself 
intrinsic,  with  knowledge  which  is  of  present  abso'- 
lute  worth  to  the  possessor  independent  of  the  form 
by  which  it  is  gained  and  retained.  Thus  one  may 
learn  with  varying  clearness,  by  means  of  a  model,  a 
drawing,  a  painting,  a  written  or  oral  description 
that  alcohol  in  large  quantities  is  injurious  to  the 
membrane  linirig  the  stomach.  This  knowledge  is 
of  intrinsic  value  to  the  individual,  and  is  the  same 
in  kind,  though  not  in  degree,  by  whatever  means  it 
has  been  gained  and  is  retained. 

Logically  distinguishable  from  these  thought 
studies — but  not  actually  separated  from  them — are 
what  may  be,  for  convenience,  termed  form  studies. 
Form  studies  include  all  the  different  modes  of 
expression:  making,  modeling,  painting,  drawing, 
written  language  (associated  with  which  are  reading 
and  spelling),  oral  language,  form,  and  number. 
The  relation  of  form  studies  to  thought  seems  to 
be  this:  external  energy,  referred  to  some  object  as 
its  source,  arouses  to  activity  the  nerve  centers,  and 
the  individual  then  vests  this  externality — the  source 
of  the  energy  —  with  color,  form,  outline,  size, 
weight,  density,  odor,  and  all  other  distinguishable 
properties,  according  to  the  sense  or  senses  through 
which  the  energy  acts.  Thus,  from  some  object, 
energy  of  a  certain  kind  reaches  a  nerve  center 
through  the  eye;  the  mind  then  vests  the  object — 
the  mediate  source  of  the  energy  --  with  color. 
Again,  the  object  is  placed  in  contact  with  the 
finger  tips;  now  the  energy,  of  which  the  object 
is  the  source,  reaches  a  nerve  center  through  the 


xii  INTRODUCTION. 

sense  of  touch  and  the  mind  vests  the  object  with 
form  and  density,  and  so  on  throughout  the  entire 
course  of  observation.  This  action  of  the  mind  may 
be  guided  somewhat  by  oral  or  written  description, 
and  by  a  careful  comparison  with  facts  already  in 
experience,  and  thus,  the  thought  gradually  becomes 
a  definite  product  in  consciousness.  At  the  sauie 
time,  as  it  becomes  a  more  closely  approximating 
mental  correspondence  to  the  source  of  the  energy, 
the  thought  clears  up  and  becomes  definite  in  con- 
sciousness. 

It  is  of  the  greatest  importance  that  all  concepts 
be  formed  in  the  mind  with  readiness,  accuracy ',  and 
completeness.  The  rate  of  mental  development  is 
absolutely  determined  by  these  'three  conditions. 
The  readiness  with  which  concepts  are  formed 
depends  upon  the  alertness,  the  all-sided  sensitive- 
ness of  the  body  to  all  the  forms  and  varieties  of 
energy,  which  impinge  upon  it  and  condition  thought. 
Keadiriess  is  dependent  primarily  and  largely  upon 
physical  and  physiological  conditions. 

Accuracy  in  forming  concepts  depends  upon  two 
things:  first,  upon  the  power  of  the  mind  to  distin- 
guish all  the  different  forms  and  varieties  of  energy 
from  each  other;  as,  for  example,  to  distinguish 
colors  from  sounds,  and  to  discriminate  between  blue 
and  pink.  Second,  it  depends  upon  the  mind's  power 
to  determine  the  limitations  of  the  energy  acting 
upon  it;  that  is,  the  mind  must  not  only  measure  or 
exactly  estimate,  in  some  way,  the  value  of  each  form 
of  energy  in  itself,  it  must  also  determine  its  relative 
value  to  all  other  forms  with  which  it  is  associated, 


INTRODUCTION.  xiii 

if  the  concept  is  to  be  clear.  Thus,  for  example, 
when  I  look  at  a  box,  if  I  properly  apprehend  and 
estimate  the  energy  received  by  the  eye,  I  get  a 
correct  idea  of  its  outline;  and  in  the  same  way  if  I 
properly  estimate  the  energy  received  when  it  is 
placed  in  contact  with  my  finger  tips,  I  get  a  cor- 
respondingly definite  idea  of  its  density  and  form. 
This  determination  of  the  limitations  of  the  energy 
is  always  done  through  a  comparison  with  a  standard 
measure.  Accuracy  is  dependent  upon  the  power  of 
judging,  and  therefore  upon  psychic  conditions.  It 
is  the  absolute  necessity  for  accuracy  that  gives  rise 
to  the  demand  for  the  mathematical  element  in  edu- 
cation. 

The  completeness  or  adequacy  of  the  concept  is 
determined  by  the  power  of  the  mind  to  grasp  and 
retain  the  relations  which  the  various  forms  and 
varieties  of  energy  bear  to  each  other.  This  is  also 
dependent  upon  psychic  conditions. 

The  function  of  the  teacher  would  seem,  therefore, 
to  be  purely  a  directive  one;  he  may  create  condi- 
tions, and,  granting  that  their  arrangement  is  the 
best  possible  (though  for  no  two  pupils,  perhaps, 
would  the  arrangement  be  equally  good),  he  has 
absolutely  nothing  beyond  a  directive  power  in  deter- 
mining  the  readiness,  accuracy,  and  completeness 
with  which  the  pupil  shall  gain  a  concept. 

The  weakest  point  in  all  teaching  of  the  present 
time  lies  in  that  part  which  relates  to  the  accuracy 
of  the  concept.  All  teaching  must  be  quantitative, 
not  alone  qualitative,  using  these  terms  in  the  labor- 
atory sense;  and  there  is,  therefore,  a  constant  and 


xiv  INTRODUCTION. 

positive  demand  for  the  mathematical  element  in 
education.  It  is  the  function  of  the  studies  of  form 
and  number  to  meet  this  demand  for  accuracy,  and 
they  can  claim  a  place  in  the  common  school  curric- 
ulum for  no  other  purpose  whatever.  This  classes 
them,  then,  from  the  pedagogical  standpoint  as  form 
studies,  as  distinguished  from  thought  studies,  and  it 
is  as  such  that  they  are  here  to  be  treated.  That 
two  multiplied  by  two  multiplied  by  two  equals 
eight  is  not  of  the  slightest  consequence  in  itself; 
but  when  it  is  said  that  the  box  is  two  feet  long,  two 
feet  wide,  and  two  feet  deep,  the  value  gf  one's 
knowledge  of  the  box  is  greatly  increased.  And 
when,  still  further,  it  is  said  that  all  the  angles  are 
right  angles  and  that  all  the  lines  are  straight  lines, 
the  mental  correspondence  is  a  close  approximation 
to  the  truth.  Of  course,  to  the  educated  mind,  dis- 
tance, angles,  and  lines  are  matters  of  experience, 
and  the  mere  mention  of  the  appropriate  terms  and 
units  is  enough  to  enable  it  to  clear  up  the  concept 
of  the  box.  But  the  case  is  different  in  the  young 
and  inexperienced,  in  whose  mind  the  notions  of  lines 
and  angles  and  judgments  of  space  and  distance  are 
almost  totally  wanting.  The  whole  question  at  issue 
is,  shall  the  attempt  be  made,  first,  by  means  of  this, 
that,  and  the  other  ingenious  device  and  by  use  of 
objects  to  which  the  child  is  more  or  less  indifferent, 
to  give  the  child  the  notions  of  lines  and  angles  and 
judgments  in  number,  to  create  in  him  a  stock  in 
trade  which  he  may  use  when  he  finds  occasion,  or 
shall  these  notions  be  developed  to  meet  the  neces- 
sities arising  from  legitimate  observation  at  the 
moment  when  the  demand  is  most  imperative? 


INTRODUCTION.  xv 

In   considering  the   question,  it  is  interesting  and 
instructive  to  note  that,  within  the  memory  of  those 
now  living,   it   was   almost  universally  held  that  all 
form  studies  should  be  pursued  in  the  beginning  for 
their  own  sake :   first,  because  of  their  extraordinary 
disciplinary  value;  and  second,  that  the  mind  might 
early  be  provided  with  a  lot  of  skeletons  upon  which 
to  build  flesh   in  after  life.     But  there  is  to-day  a 
considerable  number  of  teachers,  and  the  number  is 
rapidly    increasing,   who    believe   that    reading,    for 
example,  need  not  be  taught  except  as  the  necessities 
of  developing   thought   demand  it,  and  yet,  that  it 
may  be  thus  taught  well;  that  to  teach  spelling  it  is 
not  necessary  to  isolate  all  the  words  in  the  language 
and  write  them  in  columns  in  a  separate  book  to  be 
conned  and   committed;    who   believe    that   enough 
practice  to  teach    writing,    drawing,    painting,    and 
modeling  will  come  in  the  proper  use  of  the  material 
used  in   connection   with   legitimate  thought   work. 
Some  teachers  have  worked  out  the  problem  in  one 
direction  and  some   in   another;  very   few  or   none 
have  carried  out  the  principle  along  all  lines  of  form 
work.     Enough  has  been  done,  however,  to  establish 
the  validity  of  the  principle  and  to  show  its  practi- 
cability in  connection  with  all  the  subjects  named. 
As  to  tangible   results,  there  has   been,  perhaps,  as 
much  failure  as  success;  but,  if  there  has  been  success 
in  one  instance  even,  and  that,  too,  only  under  ideal 
conditions,  the  validity  of  the  principle  is  established, 
the  true   ideal  is  furnished,  and  all  we  have  to  do  is 
to  work  as  best  we  may  toward  it.     The  failures  have 
been   wholly   due  to  lack  of  skill  in  presenting  the 


xvi  INTRODUCTION. 

thought,  or  in  the  failure  on  the  teacher's  part  to 
grasp  the  real  scope  of  the  thought  to  be  presented. 

The  only  subject  which  has  not  at  this  time  yielded 
to  the  operation  of  the  principle  just  enunciated  is 
number.  Arithmetic — and  form  also  to  a  less  degree 
— more  strongly  than  any  other  subject,  stands 
intrenched  in  the  dogmas  and  traditions  of  the  past. 
So  long  has  it  been  enthroned  in  every  schoolhouse, 
and  in  the  heart  of  every  teacher,  as  the  great  sub- 
ject to  be  taught,  it  now  stands  aloof  and  apart  in  a 
state  of  almost  complete  isolation.  When  one  looks 
back  over  his  school-days,  no  other  subject  looms  up 
in  such  proportions  as  arithmetic.  It  is  the  one 
thing  which  consumed  his  time  and  absorbed  his 
energy.  Goaded  on  by  the  promise  of  future  reward, 
we  unceasingly  and  unlovingly  toiled.  But  now, 
when  in  later  years  we  stretch  out  our  hands  to  seize 
the  promised  reward,  we  find  it  turns  to  ashes.  It 
is  no  wonder  then  that  an  outraged  generation  grown 
to  the  estate  of  manhood,  should  cry  out  against 
arithmetic  and  seek  to  drive  it  almost  wholly  from 
our  schools.  And,  still  further,  it  is  proclaimed  that 
the  time  spent  upon  number  in  the  schools  is  wholly 
out  of  proportion  to  the  demand  made  for  its  appli- 
cation in  after  life;  that,  while  little  was  received, 
now  Heaven  be  praised,  less  still  is  needed;  and  the 
conclusion  in  either  case  is  that  the  time  given  to 
arithmetic,  number  teaching,  must  be  reduced. 

It  would  be  most  interesting  to  stop  here  and  scan 
the  pages  of  the  history  of  education  to  find  how  it 
is  that  arithmetic  gained  the  prestige  it  has  so  long 
enjoyed.  The  reason  is  clear.  The  magnificent 


INTROD  UCTION.  xvii 

achievements  in  science,  through  the  application  of 
mathematics,  of  such  men  as  Kepler,  Newton,  La 
Place  and  others,  gave  to  humanity  such  splendid 
ideas  of  the  members  and  forces  of  this  universe,  and 
rendered  our  knowledge  of  them  so  clear  and  definite, 
that  the  world  has  ever  since  been  awed  almost  into 
worship  of  even  the  means  they  employed.  Think 
of  the  richness  which  mathematics  possessed  for  such 
a  man  as  Newton !  His  every  calculation  fixed  for  him 
a  star  in  the  heavens;  it  set  the  time  ani  places  of 
the  planets,  and  measured  the  force  which  holds 
them  swinging  forever  in  their  orbits.  By  the  aid 
of  mathematics,  Newton  was  able,  more  than  any 
other  man  from  the  dawn  of  creation  down  to  his 
day,  to  penetrate  the  remote  recesses  of  this  universe 
and  to  read  the  secrets  of  the  Almighty. 

Turn  now  from  the  contemplation  of  such  a  mind, 
filled  with  this  orderly  array  of  knowledge  gathered 
from  every  corner  of  the  universe,  to  a  consideration 
of  the  store  in  our  minds.  What  has  our  mathe- 
matics done  for  us  ?  Has  it  opened  up,  and  rendered 
clear  for  us,  anything  in  this  magnificent  world 
about  us?  Did  the  study  of  mathematics  give  us 
any  clearer  notions  of  the  forces  that  focus  upon  us 
and  condition  our  existence  ?  Did  our  arithmetic  put 
anything  into  our  lives  which  gave  us  a  broader  and 
better  outlook  into  nature,  and  rendered  our  existence 
freer  from  superstition  and  more  neighborly  with  the 
truth  ?  In  so  far  as  it  has  failed  to  do  these  things, 
we  have  been  the  victims  of  a  mistake  in  teaching. 

That  there  should  be  any  attempt  to  decry  arith- 
metic teaching  in  the  schools,  brings  us  face  to  face 


x  viii  7Ar  TROD  UCTION. 

with  a  desperate  situation.  Those  who  believe  that 
they  see  in  the  different  studies  of  the  common  school 
the  necessary  and  organic  elements  of  a  symmetric 
whole,  must  push  forward  to  the  rescue  before  some 
iconoclast  rises  from  the  long-suffering  public  and  by 
some  arbitrary  act  deprives  us  of  the  power  to  organ- 
ize the  reform.  Those  in  the  past  who  gave  mathe- 
matics its  place  of  honor  among  studies  were  driven 
to  the  study  by  their  thoughts  about  the  universe. 
By  means  of  mathematical  calculations,  their  indis- 
tinct notions  became  clear  and  definite  ideas.  So 
should  it  be  with  the  pupils  in  the  public  schools; 
all  thought  studies  actually  demand  mathematical 
work  that  thought  itself  may  become  clear.  It  is  the 
function  of  form  and  number  study — that  is  of  the 
mathematical  element  in  education — to  give  accuracy 
and  exactness  to  ideas;  to  render  hazy  notions  clear, 
and  to  evolve  the  definite  from  the  indefinite.  The 
man  who  says  that  he  can  go  through  any  and  all 
walks  of  life  without  this  mathematical  element  as 
safely  as  he  can  with  it,  is  most  blindly  and  grossly 
self-deceived.  Nearly  all,  if  not  all,  the  failures  of 
life  come  to  us  because  at  some  point  in  the  train  of 
our  calculations  our  ideas  were  not  exact.  The  reason 
for  our  neglect  in  this  direction  is  that  we  were  not 
led  to  see  the  value  of  such  accuracy  in  quantitative 
work  when  in  school.  Almost  all  school  exercises 
are  qualitative  only;  they  do  not  demand  definite 
amounts  of  anything.  Despite  the  fact  that  arith- 
metic has  in  the  past,  and  does  now  as  a  rule  take  far 
more  than  its  share  of  programme  time,  yet  it  may 
be  safely  affirmed  that  true  education  in  accuracy, 


INTRODUCTION.  xix 

the  cultivation  of  the   mathematical  powers  of  the 
mind,  has  been  and  is  grossly  neglected. 

The  long  isolation  of  number  work  from  every- 
thing else  has  not  only  been  hurtful  to  all  other  sub- 
jects thus  deprived  of  its  assistance;  it  has  proved 
to  be  terribly  self-destructive.  In  trying  to  preserve 
itself  upon  its  pedestal  of  self-conceit  and  self-suffi- 
ciency, it  has  been  driven  to  most  absurd  lengths  to 
obtain  materials  for  subject-matter,  and  it  has  pressed 
upon  teachers  methods  of  instruction  that  in  many 
cases  are  simply  senseless.  It  requires  but  a  passing 
glance  at  any  arithmetic  that  one  may  pick  up  to  see 
that  the  subject-matter  in  arithmetic  is  as  bad  or 
perhaps  worse  than  it  ever  was  in  the  case  of  read- 
ing, drawing,  or  writing.  It  is  not  an  exaggeration 
to  say  that  at  least  ninety  per  cent,  of  all  the  exer- 
cises given  in  an  average  arithmetic  fall  into  one  or 
the  other  of  two  classes :  first,  those  which  deal  wholly 
with  abstract  operations,  and  second,  those  which 
deal  with  material  absolutely  outside  the  experience 
of  the  pupil.  A  few  examples  will  illustrate  this  point. 
Open  any  arithmetic  and  count  the  weary  pages  of 
such  problems  as  "What  is  -J  of  6  ?  f  of  9  ?  4  +  8=  ? 
13— 4-?  4  +  J=?  £  +  }=?  2|— 1=^  ad  nauseam. 
It  serves  no  purpose  for  the  teacher  to  say  that  he 
can  create  and  sustain  an  interest  in  such 
work.  Everyone,  doubtless,  has  been  very  much 
interested  in  just  such  problems ;  but,  if  they  are  of 
intrinsic  value,  then  why  is  it  that  all  interest  in 
them  is  lost  the  moment  the  pupil  reaches  the  years 
of  reason  and  accountability  ?  A  subject  of  intrinsic 
value  never  loses  its  interest.  We  gain  a  little  from 


xx  INTRODUCTION. 

it  when  we  are  young,  and  that  interest  deepens  and 
intensifies  with  age.  The  truth  is,  the  young 
mind  is  so  inherently  active,  it  is  so  ready  to  grasp 
everything,  that  we  frequently  mistake  the  buoyancy 
of  its  self -activity  for  genuine  interest  in  the  subject 
in  hand. 

Turning  now  to  the  second  class  of  problems 
alluded  to  above,  namely,  those  which  deal  with 
material  beyond  the  experience  of  the  pupil,  the 
same  dreary  waste  of  pages  may  be  found.  It  is 
within  the  bounds  of  truth,  perhaps,  to  say  that  nine- 
tenths  of  all  the  so-called  concrete  problems  found 
in  our  arithmetics  deal  with  questions  of  values.  This 
is  a  mistake  as  fundamental  as  it  is  singularly  per- 
verse and  unfortunate,  as  a  little  consideration  of 
the  subject  of  values  will  show.  Value  is  wholly 
relative,  and  it  grows  out  of  the  fact  that  man  is  a 
social  being.  From  the  very  nature  of  man's  social 
relations  there  must  arise  necessities  for  exchange 
among  the  different  members  of  the  community,  and 
thus  business  relations  are  established,  and,  growing 
immediately  out  of  this  is  the  question  of  value. 
Now  it  is  universally  conceded  that,  while  adult  man 
willingly  subjects  himself  to  the  laws  which  the 
necessities  of  his  social  relations  place  upon  him,  the 
child  does  not,  at  once,  recognize  such  obligations. 
And  since  his  notion  of  business  necessarily  develops 
much  later,  it  follows  that  his  idea  of  value  under 
ordinary  circumstances  must  be  late  in  maturing. 
This  is  merely  the  statement  of  a  fact  with  which  all 
are  more  or  less  familiar.  An  average  third-grade 
boy  on  the  south  side  of  a  building  on  a  warm  spring 


INTRODUCTION.  xxi 

day  would  not  exchange  his  pocketful  of  marbles  for 
a  corner  lot  unless  lie  saw  immediate  prospect  of 
reconverting  it  into  marbles  again.  And  yet  that 
same  boy  through  all  time  has  been  expected  to  solve 
problems  relating  to  the  sale  of  lands  and  estates 
with  all  the  ease  of  a  real-estate  agent  of  long 
experience.  They  are  not  much  older  when  they 
are  expected  to  solve  problems  relating  to  banking, 
taxation,  insurance,  and  stock  exchange,  the  real 
nature  of  which  they  can  have  absolutely  no  con- 
ception whatever. 

It  will  be  maintained,  however,  that  the  notion  of 
value  must  be  developed.  This  is  true,  but  let  no 
one  deceive  himself  by  supposing  that  he  is  develop- 
ing the  idea  of  value  in  his  pupils  when  he  is  having 
them  solve  problems  in  which  incomprehensible 
values  are  handled.  Nor  can  the  teacher  materially 
hasten  the  time  when  the  idea  of  value  can  be  gained. 
It  depends  absolutely  upon  experience,  and,  therefore, 
requires  time  and  can  come  only  with  age.  The  value 
of  a  dollar  is  known  only  when  it  has  been  earned. 
The  time  is  certainly  not  perceptibly  hastened  by 
early  introduction  of  toy  money  and  imaginary 
bargain  counters.  These  devices  have  about  as  much 
to  do  with  the  notion  of  developing  value  in  the 
mind  of  the  pupil  as  the  skin  of  a  stuffed  monkey 
has  with  developing  an  idea  of  the  South  American 
fauna.  Most  of  such  devices  are  nothing  but  the 
stuffed  monkeys  of  mathematids.  This  fatal  mistake 
of  filling  arithmetics  with  purely  abstract  problems, 
and,  a 'so,  the  so-called  concrete  problems  which  deal 
with  incomprehensible  material,  has  reduced  the 


xxii  INTRODUCTION. 

learning  of  arithmetic  on  the  part  of  the  pupil  to  the 
memorizing  of  a  string  of  disconnected  exercises 
which  can  neither  be  remembered  nor  applied  because 
they  are  not  associated  in  the  mind  with  any  intrinsic 
thought,  and  it  has  driven  the  instructor  to  employ 
a  vast  multitude  of  catchpenny  devices  for  the  pur- 
pose of  teaching  a  few  very  simple  processes.  It  is 
one  of  the  greatest  monstrosities  of  modern  educa- 
tion that  the  application  of  processes  so  few  in 
number,  and  so  simple  as  those  in  arithmetic,  should 
be  so  little  known  and  so  poorly  understood  by  both 
pupil  and  teachers. 

Just  how  much  number  work  must  go  with  science 
work  is  the  question  that  must  now  be  considered. 
To  be  sure,  it  is  too  much  to  say  that  all  mathe- 
matics must  be  science  mathematics;  for  every  sub- 
ject which  demands  accuracy  in  thought  must  of 
necessity  furnish  mathematical  material  of  some  kind; 
but  it  is  not  too  much  to  affirm  that  all  science 
must  be  mathematical  science.  Actual  advance  in 
science  work  is  not  possible  without  the  introduction 
of  the  mathematical  element  of  accuracy  in  quanti- 
tative work.  The  children  may  observe  a  great  deal, 
but  they  will  not  progress  unless  they,  in  the  appro- 
priate way,  accurately  measure  as  they  go.  As 
science  work  is  now  done,  in  most  cases,  the  pupils 
are  getting  a  great  deal  of  color  work  and  written 
and  spoken  language;  but  they  are  not  getting  exact 
and  definite  concepts  *  because  the  mathematical  ele- 
ment is  almost  wholly  wanting.  They  are  in  the 
precise  condition  of  one  who  learns  the  color  and 
kind  of  material  in  a  box,  but  learns  nothing  of  its 


IN  TROD  UCTION.  xxiii 

exact  form,  size,  or  weight.  Their  written  and  spoken 
language,  and  to  some  extent  their  drawings,  show 
this  in  the  great  paucity  of  mathematical  terms  and 
in  the  lack  of  exact  proportion  of  parts.  In  speak- 
ing or  writing  they  say  "few,"  "many,"  "some," 
"about,"  "nearly,"  "somewhat,"  "I  think,"  "I 
believe,"  "I  should  say,"  etc.,  all  of  which  ex  res- 
sions  and  terms  indicate  a  lack  of  clearness  and 
denniteiiesg  of  thought.  They  are  seldom  confident 
enough  in  their  work  to  make  a  direct  and  unquali- 
fied assertion  respecting  any  observation.  This  tends 
to  make  the  observation  more  lax,  and  forms  in  the 
pupils  ruinous  habits  of  carelessness  and  inexact- 
ness. 

It  is  one  thing  to  point  out  an  inherent  weakness 
in  any  system  of  instruction,  but  it  is  another  to 
suggest  a  remedy,  and  usually  a  much  more  difficult 
thing  still  -to  apply  it.  The  ability  to  teach  the 
arithmetic,  in  connection  with  any  science  work, 
which  is  necessary  to  render  the  outline  and  details 
of  the  experiment  or  observation  clear,  presupposes 
the  clearest  possible  insight  on  the  part  of  the 
teacher  into  the  central  thought,  point,  and  scope  of 
that  experiment  or  observation.  Failing  in  this  depth 
of  insight,  the  teacher  will  not  feel  the  demand  for 
number  (which  is  only  another  way  of  saying  that 
he  sees  nothing  to  number),  and  all  problems  will 
be  given  at  random,  and  consequently  they  will  not 
help  to  clarify  and  develop  that  central  thought. 
In  order  to  understand  more  clearly  the  relation  of 
number  to  science  work,  it  is  necessary  at  this  point 
to  inquire  into  the  nature  of  the  chief  operations  in 
arithmetic. 


xxiv  INTRODUCTION. 

The  mathematics  in  connection  with  science  work 
naturally  divides  itself  into  two  parts.  These  are, 
first,  what  pertains  to  the  collection  of  accurate  data, 
and  second,  that  which  pertains  to  comparisons 
necessary  in  making  generalizations.  By  the  col- 
lection of  accurate  data,  it  is  meant  that  the  pupil 
shall  in  every  case  find  by  the  appropriate  means 
the  exact  limitation  of  his  observations.  This  may 
be  illustrated  as  follows:  if  he  is  studying  the  con- 
stituents of  soils,  he  must  not  be  permitted  to 
say,  "  It  is  largely  sand  or  gravel,"  or  that  the 
organic  matter  is  small  in  amount,  but  he  must  be 
required  to  employ  such  means  as  will  show  him 
the  sand,  gravel,  etc.,  in  definite  and  exact  amounts. 
Again,  in  studying  the  color  of  butterflies,  for 
instance,  in  its  relation  to  the  environment,  the 
pupil  must  not  be  allowed  to  put  his  results  in 
the  usual  indefinite  way,  "  I  think  in  most  cases  the 
butterfly  seeks  protective  surroundings,"  but  he 
must  be  required  to  say  in  how  many  cases  he  has 
seen  the  butterfly  actually  do  so.  In  studying  the 
growth  of  plants  he  must  not  be  allowed  to  say, 
"The  tree  averages  about  so  much,"  but  he  must  by 
actually  measuring  find  out,  as  closely  as  may  be, 
what  the  average  growth  is.  In  short,  the  first 
question  which  both  teacher  and  pupil  must  have 
uppermost  in  mind,  when  contemplating  any  experi- 
ment or  observation,  is,  "  What  is  the  appropriate 
means  of  measuring  which  will  enable  me  to  pre- 
cisely determine  the  limit  of  my  observations  in  this 
case." 

After   the    data    have    been    collected    by    means 


INTRODUCTION.  xxv 

appropriate  to  the  nature  of  the  subject  and  the 
capacity  of  the  child,  the  work  of  comparison 
begins.  This  is  the  fruitful,  the  really  educative 
part  of  the  work.  The  collection  of  data  gives  skill 
and  requires  nicety  in  manipulation,  it  is  disciplin- 
ary, but  it  is  not  educative  in  a  broad  sense.  It 
does  not  give  the  broad  concepts  that  come  only 
from  comparing  results  so  collected. 

In  making  comparisons  there  may  be  recognized 
four  modes,  each  distinct  in  character  from  the 
other;  nevertheless,  they  are  modes  of  comparison 
because  they  each  so  present  data  to  the  mind  that 
the  relations  between  them  may  be  seen.  These 
four  modes  in  their  cumulative  complexity  also  bear 
a  natural  relation  to  the  development  of  the  child's 
mind.  The  first  mode  of  comparison  which  a  child 
uses  is  where  all  the  qualities  are  considered  as 
wholes.  Under  this  mode,  the  genesis  of  the  four 
fundamental  operations  as  means  of  comparison  may 
be  illustrated  by  the  following  examples:  the  child 
has,  for  instance,  two  sticks  of  different  lengths;  his 
very  first  comparison  respecting  length  is  expressed 
by  saying  either,  "  One  is  longer  than  the  other,"  or 
"  One  is  shorter  than  the  other."  In  the  first  case 
he  is  looking  at  the  long  stick  and  thinks,  "  It  is 
like  the  short  stick  with  more  to  it."  This  is  his 
initial  thought  in  addition.  In  the  second  case  he 
is  looking  at  the  short  stick  arid  thinks,  "  It  is  like 
the  long  stick  with  part  of  it  taken  away."  This  is 
his  initial  thought  in  subtraction.  Very  soon  he 
is  able  to  say  exactly  how  much  must  be  added  to 
the  one  or  taken  from  the  other,  and  at  that  stage 


xx  vi  INTRODUCTION. 

the   definite  processes   of    addition  and   subtraction 
begin. 

A  little  later,  as  he  looks  at  the  short  stick,  he 
thinks,  for  instance,  "  If  I  could  put  two  or  more  of 
my  short  sticks  together,  they  would  then  be  like 
my  long  stick."  This  is  his  initial  step  in  multipli- 
cation. Or,  looking  at  the  long  stick,  he  may  think, 
"  If  I  could  cut  it  into  two  or  more  equal  pieces, 
I  should  then  have  two  or  more  pieces  like  the  short 
stick."  This  is  the  beginning  of  division.  In  these 
first  steps  in  comparison  the  child  naturally  employs 
whole  numbers  in  the  four  fundamental  operations 
given  in  the  books  as  addition,  subtraction,  multi- 
plication, and  division. 

The  second  mode  of  comparison  is  by  considering 
one  of  the  quantities  directly  as  a  part  of  the  other. 
The  child  now  says,  "  The  short  stick  is  one-half  the 
length  of  the  other."  This  is  his  first  step  in  par- 
tition, and  at  this  stage  he  is  ready  to  begin  the  study 
and  use  of  fractions. 

In  the  third  mode  of  comparison,  the  child  may 
use  either  quantity  as  the  standard,  but  he  must  be 
able  to  conceive  of  it  as  being  represented  by  unity. 
Thus  in  two  trees,  if  one  is  twenty  feet  high  and 
another  eighty  feet,  he  must  not  only  be  able  to  see 
that  one  is  sixty  feet  higher  than  the  other;  that  it 
is  four  times  the  height  of  the  other;  that  the  shorter 
is  one-fourth  the  height  of  the  taller,  but  also  that, 
if  the  shorter  is  represented  by  one,  the  longer  is 
represented  by  four;  also,  if  the  longer  is  one, 
the  shorter  is  one-fourth.  Thie  mode,  including  all 
of  what  is  given  under  ratio  and  proportion,  is  of 


INTRODUCTION 

more  difficult  application  than  either  of  the  others 
arid  should  be  introduced  later  in  the  work  of  the 
pupil,  but  not  so  late  as  might  be  inferred  from  the 
place  usually  assigned  to  it  in  books  on  arithmetic. 

In  the  fourth  mode  of  comparison  the  pupil  must 
be  able  to  grasp  what  has  been  described  in  the  first, 
second,  and  third  modes,  and  must,  besides,  be  able 
to  conceive  of  one  of  the  quantities  being  represented 
by  one  hundred.  Under  this  mode  are  included  all 
the  operations  that  belong  to  percentage  in  the  text- 
books. If,  in  the  examination  of  soils,  he  finds  ten 
grams  of  gravel  in  fifty  grams  of  soil,  the  pupil  will 
say  that  if  the  soil  is  represented  by  one  hundred 
the  gravel  will  be  represented  by  twenty;  that  is, 
twenty  per  cent,  of  the  soil  is  gravel. 

From  this  discussion,  it  will  be  seen  that,  as  early 
as  the  pupil  is  able  to  make  a  definite  observation, 
he  has  at  his  command,  and  does  in  fact  naturally 
employ,  a  mode  of  comparison  corresponding  to  his 
stage  of  development;  also,  that  each  mode  of  com- 
parison rests  upon  a  corresponding  mathematical 
operation;  and  further,  these  operations  tend  to  clear 
up  and  define  his  ideas  of  the  subject  he  studies.  It 
will  also  be  observed  that  with  the  exception  of 
such  exercises  as  are  intended  to  be  used  for  the 
purpose  of  fixing  the  units  of  measurement  the 
whole  of  arithmetic  is  included  under  these  four 
great  modes  of  comparison.  It  follows,  that  any 
subject  or  subjects  which  can  furnish  a  sufficient 
amount  of  legitimate  material  to  provide  problems 
enough  in  these  four  modes  of  comparison,  will 
meet  even  the  present  demand  for  arithmetic  in 


INTRODUCTION. 

the  schools.  The  amount  of  material  actually 
demanding  such  number  work,  which  may  be  gathered 
from  the  beginning  in  the  domain  of  natural  science, 
is,  practically,  only  determined  by  the  intelligence  of 
the  teacher  in  directing  his  pupil,  and  by  the  limita- 
tions imposed  by  adverse  conditions  under  which 
most  teachers  labor.  The  test  which  the  teacher 
must  apply  to  such  problems  is,  first,  are  they  good 
science?  That  is,  will  their  solution  tend  to  clear  up 
the  concept  sought?  And  second,  are  they  good  arith- 
metic? That  is,  do  they  involve  any  absurdity  in 
calculation?  If  they  fulfill  legitimate  demand  of 
science,  and  do  not  outrage  the  canons  of  number, 
they  should  be  admitted  as  properly  educative  factors. 
Before  leaving  the  subject,  a  word  should  be  said 
about  the  method  of  teaching  upon  this  new  basis. 
New  wine  must  not  be  put  into  old  bottles.  The 
same  principle,  precisely,  holds  in  this  case  that  is 
already  recognized  to  some  extent  and  obeyed  in 
teaching  other  subjects.  Formerly,  spelling,  read- 
ing, etc.,  were  taught  as  ends;  now  thought  is  the 
end  and  they  are  incidental.  The  fatal  mistake  that 
has  been  made  is  in  teaching  the  thought  and  making 
the  spelling,  etc.,  accidental.  There  is  a  mighty 
difference  between  the  incidental  teaching  of  form 
subjects  and  the  accidental  teaching  of  them.  So 
now,  in  this  number  work,  the  teacher  must  clearly 
work  for  the  intrinsic  thought  and  make  the  teach- 
ing of  the  arithmetical  operations  incidental,  but  by 
no  means  accidental.  These  processes  must  be  just 
as  thoroughly  taught  as  ever  before;  they  will  be 
more  thoroughly  taught  in  far  less  time,  too,  when 


INT  ROD  UCT10N.  xx  i  x 

touchers  really  grasp  the  subject  matter  in  hand. 
Tlu>  reason  for  this  faith  has  its  source  in  the  peda- 
gogical fact  that  in  the  new  order  of  things  the  in- 
trinsic thought  of  the  subject  will  demand  the  opera- 
tions; and  the  pupil,  if  properly  directed  by  the 
teacher,  will  feel  this  actual  demand,  and  his  mind 
will  work  for  them  at  its  highest  possible  tension. 
We  lose  enormously  by  working  at  a  subject  with 
our  pupils  when  their  minds  have  a  low  tension — a 
low  potential,  to  borrow  a  term  from  physics.  We 
all  know  from  experience  and  observation  how 
quickly  and  strongly  even  seemingly  dull  minds 
grasp  facts,  principles,  and  operations  when  they  are 
rendered  really  alert  by  an  actual  desire  to  get  the 
thought.  This,  then,  is  the  first  duty  of  the  teacher 
in  the  present  case:  stimulate  the  mind  to  its  great- 
est activity  with  the  subject  matter,  and  then  defi- 
nitely direct  this  activity  by  means  of  the  various 
arithmetical  operations.  Questions  prepared  in  con- 
nection with  the  science  work  from  any  other  motive 
will  be  utterly  useless  and  they  will  render  the  pupils 
as  listless  as  the  most  arid  arithmetic  ever  used. 


METRIC  TABLES. 


MEASURES  OF  EXTENSION. 
The  Meter  is  the  unit  of  length,  and  is  equal  to 
39.37  in.,  nearly. 

TABLE. 

Metric  Denominations.  U.  S.  Value. 

1  Millimeter  =      .03937079  in. 

10  Millimeters,    mm.  =1  Centimeter  =      .3937079  in. 

10  Centimeters,   cm.  =1  Decimeter  =    3  937079  in. 

10  Decimeters,    dm.  =1  Meter  =  39.37079  in. 

10  METERS,  M.  =1  Dekameter  =  32.808992  ft. 

10  Dekameters,  Dm.  =1  Hectometer  =  19  927817  rd. 

10  Hectometers,  Hm.  =1  Kilometer  =      .6213824  mi. 

10  Kilometers,    Km.  =1  Myriameter(Jfm)=    6.213824  mi. 

The  Are  is  the  unit  of  land  measure,  and  is  a 
square  whose  side  is  ten  meters,  equal  to  a  square 
dekameter,  or  119.6  square  yards. 

TABLE. 

1  Centiare,  ca.    =(1  Sq.  Meter)      =      1.196034  sq.  yd. 
100  Centiares,  "        =1  Are  =  119.6034  sq.  yd. 

100  ARES         A.     =  1  Hectare  (Ha.)=      2.47114  acres. 

MEASURES  OF  CAPACITY. 

The  Liter  is  the  unit  of  capacity,  both  of  -Liquid 
and  of  Dry  Measures,  and  is  a  vessel  whose  volume 
is  equal  to  a  cube  whose  edge  is  one-tenth  of  a  meter. 
equal  to  1.05673  qt.  Liquid  Measure,  and  .9081  qt. 
Dry  Measure, 

XXX 


METRIC  TABLES. 


XXXI 


TABLE. 


10  Milliliters,  ml 

10  Centiliters,  cl. 

10  Deciliters,  dl. 

10  LITERS,  L. 

10  Dekaliters,  Dl. 

10  Hectoliters,  HI. 

10  Kiloliters,  Kl 


=  1  Centiliter. 

=  1  Deciliter. 

=  1  Liter. 

=  1  Dekaliter. 

=  1  Hectoliter. 

=  1  Kiloliter,  or  Stere. 

=  1  Myrialiter  (.Ml) 


The  Hectoliter  is  the  unit  in  measuring  liquids, 
grain,  fruit,  and  roots  in  large  quantities. 

MEASURES  OF  WEIGHT. 

The  Grain  is  the  unit  of  weight,  and  equal  to 
the  weight  of  a  cube  of  distilled  water,  the  edge  of 
which  is  one  hundredth  of  a  meter,  equal  to  15.432 
Troy  grains, 

TABLE. 


10  Milligrams, 
10  Centigrams, 
10  Decigrams, 
10  GRAMS, 
10  Dekagrams, 

10  Hectograms, 

10  Kilograms, 
10  Myriagrams,orMg 
100  Kilograms, 
10  Quintals,  or 
1000  KILOS 


U.  S.  Value. 

mg. 

=1  Centigram  = 

15432+gr.  Troy 

eg. 

=1  Decigram    = 

1.54324+    " 

dg. 

=1  Grain        = 

15.43248+    " 

Q. 

—1  Dekagram  = 

.35273+oz.  Avoir 

Dg. 

=1  Hectogram= 

3.52739+  "      " 

Hg. 

i  j  Kilogram  \ 
=1\of  Kilo,  J- 

2.20462+lb.     " 

Kg. 

=1  Myriagram= 

22.04621+  "      " 

=1  Quintal      =  220  46212+ 


™ 


^2204.62125    " 


COLORS  OF   INSECTS. 


The  brilliant  coloring  of  many  insects  that  may  be 
easily  found  renders  this  department  of  nature  study 
of  interest  to  the  younger  as  well  as  to  the  more  ad- 
vanced pupils.  That  the  colors  displayed  perform 
some  important  function  in  the  life  of  the  insect  can 
not  be  a  matter  of  doubt;  but  what  their  full  import  is 
can  hardly  be  called,  as  yet,  a  settled  question.  In 
many  instances,  the  colors  serve  as  a  protection 
through  their  similarity  to  or  harmony  with  the  sur- 
roundings, while  in  other  cases  this  is  not  very  evident 
— the  colors  being  rather  an  advertisement  of  the 
insect's  whereabouts.  This  is  probably  for  the  bene- 
fit of  its  mate.  The  question  of  adaptation  to  en- 
vironment is  one  which  is  almost  immediately  raised, 
and  here,  as  with  plant  life,  it  is  one  of  great  interest. 

The  number  selected  for  study  must  vary  with  the 
different  conditions  under  which  the  work  is  done, 
but  it  should  always  be  as  large  as  possible  so  that 
the  errors  of  observation  may  be  minimized  in  the 
final  result.  The  outcome  of  the  work,  if  well  done, 
will  be  to  lead  the  pupils  a  little  nearer  the  laws  of 
life  which  govern  all  living  things,  and  to  render  the 
pupil  a  little  cautious  about  accepting  assertions 
until  he  has  applied  the  test  of  his  experience. 

The  small  yellow  butterfly  (Colias)  and  the  large 
1 


NUMBER  WORK.  [September 

brown  rnilk-weed  butterfly  (Danais)  are  abundant, 
and  make  excellent  objects  for  study. 

I.     WHOLE  NUMBERS. 

1.  In  fifty  observations,  how  many  times  have 
you  seen  the  same  kind  of  butterfly  alight  upon 
flowers  whose  colors  are  protective,  i.e.,-  which  tend 
to  make  the  insect  inconspicuous? 

2.  In  how  many  instances  were  the  flowers  of 
the  same  color  as  the  insect? 

3.  In  how  many  instances  were  the  flowers  of 
such    colors    as    to    merely    harmonize    with    the 
insect's  colors? 

4.  How  many  times  did  they  alight  upon  plants 
or  in  situations  where  their  colors  rendered  them 
conspicuous  ? 

5.  Compare  the  results  obtained  in  (1)  and  (4); 
how  many  more  in  one  case  than  the  other? 

6.  In  twenty-five  observations,  how  many  times 
have  you  seen  the  same  butterfly  alight  in  protect- 
ive situations? 

7.  In  how  many  cases  was  the  insect  rendered 
more  conspicuous  by  its  surroundings? 

8.  Compare  the  results  obtained  in  (6)  and  (7) ; 
which  is  in  excess,  and  how  much  ? 

9.  Observe  each  one  of  ten   different  kinds  of 
butterflies  alight  twenty-five  times;  which  exceeded, 
and  how  much,  those  selecting  protective  or  those 
taking  non-protective  situations  in  the  majority  of 
cases  ? 

10.  Collect  twenty-five  different  kinds  of  insects; 
how   many   are  there  whose  colors   are  especially 
protective  ? 


September]  ZOOLOGY.  3 

11.  How  many  are  there  whose  coloring  is  of 
no  special  importance? 

II.  FRACTIONS. 

1.  In  fifty  observations,  what  part  of  the  entire 
number  of  butterflies  observed  alighted  in  protect- 
ive situations? 

2.  What  part  of  the  entire  number  alighted  in 
non- protective  situations? 

3.  The  number  selecting   protective  situations 
equals  what  part  of  the  number  selecting  places 
non- protective? 

4.  What    part    of   the    entire    number    always 
selected  protective  situations? 

5.  What  part  of  the  entire  number  never  selected 
protective  situations? 

6.  Of    twenty -five    different    butterflies    of    the 
same  kind,  observe  each  one  alight  ten  times;  what 
is  the  average  number  of  times  where  the  situation 
was  protective? 

7.  What  is  the  average  of  the  number  of  times 
where  the  situation  was  non-protective? 

8.  Of  ten  butterflies   of  different  kinds,    what 
part  in  the  majority  of  cases  selected    protective 
situations  ? 

9.  Of  twenty-five  different  kinds  of  insects,  what 
part  of  the  whole  number  is  protected  by  coloring? 

10.  What  part  is  not  so  protected? 

III.  KATIO. 

1.  In  fifty  observations  upon  the  same  kind  of 
butterfly,  what  is  the  ratio  of  those  seeking  flowers 
that  have  protective  coloring  to  those  indifferent 


4  NUMBER  WORK.  [September 

to    such    conditions?     What   is    the    ratio   of  the 
latter  to  the  former?  ' 

2.  In   twenty-five   observations   upon  the  same 
butterfly,  what  is  the  ratio  of  the  number  of  times 
that  it  selected  protective  to  the  number  of  times 
that  it  selected  non-protective  situations? 

3.  In  ten  different  kinds  of  butterflies,  what  is 
the  ratio  of  those  that  selected  situations  with  pro- 
tective coloring,  in  the  majority  of  cases,  to  those 
that  selected  non-protective  places? 

4.  In    twenty-five   different     kinds    of    insects,, 
what  is  the  ratio  of  those  that  make  special  use 
of  protective    coloring   of    their   surroundings  to 
those  that'  do  not  ? 

IV.  PERCENTAGE. 

1.  In  fifty    observations,  what  per  cent  of  the 
entire  number  of  butterflies  alighted  upon  flowers 
whose  colors  rendered  them  less  conspicuous? 

2.  What  per  cent  of   the   entire   number  were 
rendered  more  conspicuous? 

3.  In    twenty-five  observations,  the  number  of 
times  the  same  butterfly  seemed  to  select  protect- 
ive situations  is  what  per  cent  of  the  whole? 

4.  What  per  cent  of  the    whole  is  the  number 
of  cases  where  insect  was  rendered  more  conspicu- 
ous by  its  surroundings? 

5.  In  ten  observations  upon  each  of  ten  different 
butterflies,  what  per  cent  selected,  in  a  majority  of 
cases,  situations  which  rendered  them  less  conspic. 
uous  when  they  alighted  ? 

6.  What  per  cent  of   the  whole  were    rendered 
more  conspicuous  by  their  surroundings? 


September]  ZOOLOGY.  5 

7.  Collect  twenty-five  different  kinds  of  insects; 
what  per  cent  of  the  number  have  protective  color- 
ing? 

8.  What  per  cent  of    the  number  do  not  have 
protective  coloring? 

9.  What  per  cent  of  the  entire  number  are  ren- 
dered more  conspicuous  by  their  colors? 

10.  What  per  cent  of  the  entire  number  have 
some  special  enemy  which  they  try  to  avoid? 


BOTANY. 


MUTUAL   RELATIONS  OF    PLANTS  AND 
ANIMALS-STUDY  OF    LEAVES. 


The  following  series  of  problems  is  designed  to 
accompany  an  autumn  study  of  leaves.  It  is  intended 
to  show  something  of  the  importance  of  the  rela- 
tions which  exist  between  leaves  and  the  insect  life 
which  swarms  upon  them  at  this  season.  An  inter- 
esting comparison  may  be  made  between  the  present 
condition  of  the  leaves  and  that  noticed  earlier  in  the 
season,  say,  during  the  month  of  June.  From  the 
large  proportion  of  leaves  found  to  be  injured,  it 
would  seem,  at  first,  as  though  the  trees  must  be 
greatly  weakened  thereby.  In  exceptional  years  this 
is  doubtless  true,  but,  that  it  is  not  uniformly  true  is 
evident  or  the  result  would  be  the  gradual  loss  of 
vitality  and  premature  death  of  the  tree.  The  almost 
perfect  balance  which  exists  between  the  demand  and 
supply  of  both  insect  and  plant  seems  to  be  largely 
favored  by  the  fact  that  the  voracious  larva?  begin 
their  feeding  comparatively  late  and,  before  they  have 
destroyed  any  considerable  amount,  the  function  of 
the  leaf  in  building  up  the  buds  and  other  new 
materials  in  the  plant  has  mainly  been  fulfilled.  It 
will  be  noticed,  too,  that  the  large  proportion  of  leaves 
injured  gives  an  indication  of  the  even  distribution 
of  the  work  of  the  insect  over  the  entire  tree,  thus 

6 


September]  BOTANY.  7 

reducing,  relatively,  the  loss  to  each  bud.  By  laying 
a  piece  of  wire  gauze  of  about  one-tenth-inch  mesh 
over  the  leaf  the  loss  to  each  may  be,  by  this  means, 
fairly  estimated  and  the  results  may  be  definitely 
stated. 

The  study  should  be  thoroughly  systematic  and 
should  conform  to  the  conditions  of  teacher  and 
pupils.  The  entire  time  and  attention  may  be  given 
to  a  single  tree  or  plant  or  to  a  set  of  the  same  kind, 
or  the  school  may  be  grouped  and  data  gathered 
from  different  kinds  of  plants  and  interesting  com- 
parisons made  between  them.  The  number  of  leaves 
to  be  used  as  a  basis  of  comparison  must  be  deter- 
mined in  each  case  by  the  amount  of  time,  the  ability 
of  the  pupils  and  by  other  conditions  under  which 
the  study  is  made. 

PROBLEMS. 

I.     WHOLE  NUMBERS. 

1.  Of  one  hundred   leaves  examined,  how  many 
have  not   been  injured  or  used  in  any  way  by  ani- 
mals? 

2.  How  many  have  been  injured? 

3.  How  many  have   been    stung  by  insects   in 
laying  their  eggs? 

4.  How  many  so  stung  have  apparently  lost  their 
usefulness  as  leaves  (i.  <?.,  have  been  swollen  into 
balls  or  other  distorted  forms)  ? 

5.  How  many   leaves   have   been   devoured,   in 
part,  as  food  by  insects  or  their  larvae? 

0.   How   many  leaves  have  been  used,  in  some 
way,  by  insects  in  making  nests  or  cocoons? 


NUMBER  WORK.  [September 

7.  Of  one  hundred  leaves  taken  from  the  oak, 
ash,   maple,   elm,   and   box-elder,   which    has    the 
greatest  number  injured?     Which  the  least? 

8.  What  is  the  difference  between  the  number 
injured  on  the  oak  and  the  number  found  injured 
upon  the  maple? 

9.  What  is  the  difference  between   the  number 
injured  found  on  the  oak  and  that  found  on  the 
ash? 

10.  What  is  the  difference  between  the  number 
injured  found  on  the  oak  and  that  found   on  the 
box-elder? 

II.     FRACTIONS. 

1.  Of  one  hundred   leaves  examined,  what  part 
has   not   been  injured  or  used  in  any  way  by  ani- 
mals? 

2.  What  part  has  been  injured  or  so  used? 

3.  What  part  of    the    entire  number  has  been 
stung  by  insects  in  laying  their  eggs? 

4.  What  part  of  the  number  stung  has  lost  the 
ordinary  leaf  form  after  being  stung? 

5.  What  part  of  the    entire  number  has   been 
devoured    partially  by   insects  or   their  larvae   as 
food? 

6.  What  part  of  the  entire  number  examined  has 
been  used  by  insects  in  nest- building  or  making 
cocoons  ? 

7  Of  one  hundred  leaves  taken  from  the  oak, 
ash,  maple,  elm,  and  box-elder,  which  has  the 
greatest  part  injured,  and  how  much  ?  Which  the 
least,  and  how  much  ? 


September]  BOTANY.  9 

8.  Of  the   entire   number  examined,    the    part 
found  injured  on  the  oak  equals  what  part  of  that 
injured  on  the  maple? 

9.  Of    the    entire   number    examined,  the   part 
found  injured  on  the  oak  equals  what  part  of  that 
found  injured  on  the  asli  ? 

10.  The  number  found  injured  on  the  oak  equals 
what  part  of  that  found  injured  on  the  box-elder? 

III.     RATIO. 

1.  In  one  hundred  leaves  examined,  what  is  the 
ratio  of  those  that  have  not  been  used  in  any  way 
by  insects  to  those  that  have  been  so  used? 

2.  What  is  the  ratio  of  the  number  of  injured 
leaves  to  the  entire  number  observed? 

3.  What  is  the  ratio  of  the  uninjured  leaves  to 
the  whole  number  observed? 

4.  Of  the  leaves  stung  by  insects,  what  is  the 
ratio  of  those   that  have  remained  unchanged  in 
form  to  the  whole  number  stung? 

5.  What  is  the  ratio  of  those  stung  that  have 
had  the  leaf-form  modified  thereby  to  those  that 
have  remained  unchanged  in  form? 

6.  The  number  of  leaves  that  have  been  used 
in  nest-building,  or' in  making  cocoons,  bears  what 
ratio  to  the  entire  number  examined? 

7.  The  number  of  leaves  found  injured  on  the 
oak  bears  what  ratio  to  the  number  found  injured 
on  the  ash? 

8.  The  number  of    injured  leaves  on  the  oak 
bears   what  ratio   to  the  number   injured  on   the 
maple  ? 


10  NUMBER  WORK.  [September 

9.  The  number  injured  on  the  oak  bears  what 
ratio  to  the  number  injured  on  the  elm? 

10.  The  number  injured  on  the  oak  bears  what 
ratio  to  the  number  injured  on  the  box-elder? 

IV.  PERCENTAGE. 

1.  What  per  cent  of  the  whole  number  of  leaves 
examined  have  been  injured  by  insects? 

2.  What  per  cent  remain  uninjured? 

3.  What  per  cent  of  the  entire  number  observed 
have  been  stung  by  insects  in  laying  their  eggs? 

4.  What  per  cent  of  the  number  stung  have  lost 
the  ordinary  leaf-form  as  a  result  of  the  injury? 

5.  What  per  cent  of  the  entire  number  have  been 
devoured  in  part  by  insects,  or  their  larvae,  as  food? 

6.  What  per  cent  of  the  entire  number  of  leaves 
examined  have    been  used  by  insects  in  making 
nests  or  cocoons  ? 

7.  In  the  oak,  ash,  maple,  elm,  and  box-elder, 
which    has    the    greatest    percentage    injured    by 
insects  ?     Which  the  least  ? 

8.  The  number  of  leaves  injured  upon  the  oak 
is  what  per  cent  of  that  found   upon  the  ash  ? 

9.  The  number  of  injured  leaves  found  upon  the 
oak  is  what  per  cent  of  that  found  upon  the  maple  ? 

10.  The  number  of  injured  leaves  found  upon 
the  oak  is  what  per  cent  of  the  number  found  upon 
the  box-elder? 


STRUCTURE   AND   COLORS   OF   FRUITS. 


In  the  structure  and  coloring  of  fruits  there  is  a 
beautiful  adaptation  of  means  to  end.  The  trans- 
formation of  the  green,  hard,  and  usually  sour,  or 
bitter,  fleshy  portion  in  many  fruits,  at  the  maturity 
of  the  seeds,  into  a  soft,  juicy,  and  palatable  pulp, 
rendered  attractive  by  beautiful  colors,  is  a  change 
full  of  meaning  to  the  plant  and  rich  in  suggestion 
to  the  student.  The  bearing  of  this  lesson  is  upon 
the  subject  of  distribution  of  seeds  and  it  should  be 
associated  with  the  lessons  on  that  subject.  The 
pupils  should  collect  a  great  variety  of  fruits  and 
then  proceed  to  group  them.  The  following  classes 
are  suggested: 

1.  Fleshy  Fruits:  such  as  the  grape,  gooseberry, 
and  cranberry. 

2.  Stone  Fruits:    such  as  the    plum,   peach,    and 
apricot. 

3.  Dry  Fruits:  such  as  the  nuts  and  the  seeds  of 
many  weeds. 

PROBLEMS. 
I.     WHOLE  NUMBERS. 

1.  How  many  different  fruits  have  you  collected  ? 

2.  How  many  are  fleshy  fruits? 

8.  How  many  in  your  collection  are  stone  fruits? 
11 


12  NUMBER  WORK.  [September 

4.  How  many  in  your  collection  are  dry  fruits? 

5.  Which  class  is  largest  and  how  much  ? 

6.  How  many  different  fruits  collected  are  col- 
ored conspicuously  ? 

7.  How  many  different  fruits  collected  are  not 
colored  conspicuously  ? 

8.  How  many  of  those  conspicuously  colored  are 
fleshy  fruits? 

9.  How  many  of  those  conspicuously  colored  are 
stone  fruits? 

10.  How  many  of  those   conspicuously  colored 
are  dry  fruits? 

11.  How  many  of  the  fruits  in  your  collection 
become  more  conspicuous  when  ripe? 

12.  How  many  are   used   as    food  before  they 
ripen  ? 

13.  What   is   the   prevalent  color  among   your 
fruits?    How  many  of  each  class  have  this  color? 

14.  How  many  of  the  different  kinds  of  highly 
colored  fruits  harmonize  with  the  foliage  of  the 
plant? 

II.     FRACTIONS. 

1.  What  part  of  your  entire  collection  is  com- 
posed of  fleshy  fruits? 

2  What  part  of  your  entire  collection  is  com- 
posed of  stone  fruits? 

3.  What  part  of  your  entire  collection  is  com- 
posed of  dry  fruits  ? 

4.  What  part  of  the  entire  collection  is  colored 
conspicuously  ? 

5.  The  stone  fruits  are  what  part  of  those  col- 
ored conspicuously  ? 


September]  BOTANY.  13 

6.  The  fleshy  fruits  ;uv  what  part  of  those  col- 
ored conspicuously  ? 

7.  The  dry  fruits  are  what  part  of  those  colored 
conspicuously? 

8.  What  part  of  your  entire  collection  becomes 
more  conspicuous  when  ripe? 

9.  What  part  is  used  as  food  before  ripe? 

10.  What  is  the  prevailing  color  among   your 
fruits?     What  part  of  the   fleshy  fruits  has  this 
color?    Of  the  stone  fruits?    Of  the  dry  fruits? 

11.  What  part  of  all  those  highly  colored  har- 
monizes with  the  foliage  of  the  plant? 

III.     RATIO. 

1.  What  is  the  ratio  of  the  stone  fruits  to  the 
entire  collection? 

2.  What  is  the  ratio  of  the  fleshy  fruits  to  the 
entire  collection  ? 

3.  What  is  the  ratio  of  the  dry  fruits   to  the 
entire  collection? 

4.  What  is  the  ratio  of  the  stone  fruits  to  the 
fleshy  fruits? 

5.  What  is  the  ratio  of   the  dry  fruits  to  the 
stone  fruits? 

0.  What  is  the  ratio  of  the    dry   fruits  to  the 
fleshy  fruits? 

7.  What  is  the    ratio  of  the  dry  fruits  to  the 
stone  and  fleshy  fruits? 

8.  What   is    the    ratio   of   those   conspicuously 
colored  to  the  entire  collection? 

9.  What    is    the    ratio    of   the    conspicuously 
colored  stone  fruits  to  the  entire  number  of  stone 
fruits? 


14  NUMBER  WORK.  [September 

10.  What    is    the    ratio   of    the    conspicuously 
colored  fleshy  fruits  to  the  entire  number  of  fleshy 
fruits? 

11.  What    is    the    ratio    of    the    conspicuously 
colored  dry  fruits  to  the  entire  collection  of  dry 
fruits  ? 

12.  What    is   the    ratio    of  the    fruits  that   are 
used  as  food  by  animals  before  they  ripen  to  the 
entire  number? 

13.  What    is    the    ratio    of  the  fruits    in    your 
collection    that    become   more   conspicuous    when 

*  they  ripen  to  the  whole  number? 

14.  What  is  the  prevailing  color  among  your 
fruits?     What    is   the    ratio    of   the    stone    fruits 
having  this  color  to  all  the   stone  fruits?     Of  the 
fleshy  fruits?     Of  the  dry  fruits? 

IV.  PERCENTAGE. 

1.  The  stone  fruits  are  what  per  cent  of  the 
entire  collection? 

2.  The  fleshy  fruits  are  what   per  cent  of  the 
entire  collection? 

3.  The    dry    fruits  are    what   per   cent   of  the 
entire  collection? 

4.  The  number  of  stone  fruits  equals  what  per 
cent  of  the  number  of  fleshy  fruits? 

5.  The  number  of  dry  fruits  equals  what  per  cent 
of  the  number  of  stone  fruits?  Of  stone  and  fleshy 
fruits  together? 

6.  The  number  of  conspicuously  colored  fruits 
equals  what  per  cent  of  the  whole  number? 

7.  The  conspicuously   colored  stone   fruits   are 
what  per  cent  of  the  entire  number  of  stone  fruits? 


September]  BOTANY.  15 

8.  The  conspicuously  colored  fleshy  fruits  are 
what  per  cent  of  the  entire  number  of  fleshy  fruits  ? 

9.  The    conspicuously    colored    dry    fruits    are 
what  per  cent  of  the  entire  number  of  dry  fruits? 

10.  The  number  of  fruits  that  are  used  for  food 
by  animals  before  they  ripen  is  what  per  cent  of 
the  entire  number? 

11.  What  per  cent  of  the    fruits  become  more 
conspicuous  as  they  ripen  ? 

12.  What    is  the   prevailing   color  among   the 
fruits?     What  per  cent  of  the  stone   fruits  have 
this   color?     Of  the    fleshy    fruits?     Of   the    dry 
fruits? 

13.  What  per  cent  of  the  highly  colored  fruits 
harmonize  with  the  foliage  of  the  plant? 


A    STUDY    OF    THE   CONSTITUENTS  OF 
FRUITS. 


It  is  the  aim  of  the  following  lessons  to  give  the 
pupils  a  definite  idea  of  the  absolute  and  relative 
amounts  of  fluid  matter,  dry  solid  matter,  organic 
matter,  and  mineral  matter,  or  ash,  of  which  some 
of  the  common  fruits  and  vegetables  are  composed. 
In  order  to  perform  the  work  required  satisfactorily, 
a  small  amount  of  apparatus  is  necessary:  a  small 
set  of  balances  with  weights  —  metric  preferred; 
physicians'  scales,  with  horn  scale-pans,  and  coin 
weights  from  twenty  grams  down  to  one  centigram, 
will  answer  the  purpose;  a  Battersea  dish  with  a 
tripod  or  retort  stand,  or  other  support  for  it,  over 
the  alcohol  or  Bunsen  flame.  It  is  also  desirable  to 
have  a  convenient  means  for  drying  the  fruits  at 
school.  This  may  be  done  by  providing  a  small  tray, 
about  one  inch  deep,  divided  by  pasteboard,  or  thin 
wooden  strips,  into  forty  or  fifty  compartments,  each 
about  one  and  one-half  inches  square.  Use  fine  wire 
gauze  for  a  bottom,  and  tack  the  same  over  the  other 
side  for  a  cover.  Mosquito  netting  may  be  substi- 
tuted for  the  gauze.  This  tray  will  give  each  pupil  a 
compartment  for  his  fruit,  and,  with  a  little  care,  the 
work  of  an  entire  room  may  be  nicely  dried.  The 
trav  may  be  hung  in  the  sun  and  the  gauze  will 
enable  evaporation  to  proceed  quite  rapidly.  In 

16 


September]  BOTANY.  17 

most  cases,  perhaps,  the  teacher  will  have  but  one 
set  of  apparatus  to  begin  with,  but,  for  a  beginning, 
this  is  sufficient.  Take  one  fruit  or  vegetable  after 
another  and  assign  different  parts  of  the  work  to 
different  pupils,  and,  with  a  little  care  and  patience, 
data  enough  will  soon  be  gathered  to  enable  the 
pupils  to  have  a  fair  idea  of  the  component  parts  of 
those  examined. 

With  beginners,  and  with  pupils  in  the  lower 
grades,  it  will  be  sufficient  to  show  how  much  fluid 
and  solid  matter  the  fruit  contains,  and  large  pieces 
should  be  used;  but  with  pupils  more  advanced, 
smaller  amounts  should  be  used  and  all  four  parts 
determined. 

Proceed  as  follows: 

1.  Weigh  out  a  definite  amount,  say,  five  grams  of 
the  fresh  fruit. 

2.  Dry  it  until  it  no  longer  loses  weight — testing 
from  time  to  time.     It  must  not  be  subjected  to  great 
heat,  or  charring  will  take  place.    This  gives  the  dry 
solid  matter. 

3.  Powder  the  dry  solid  matter*  and  weigh  a  defi- 
nite amount  of  it  and  place  this  in  the  Battersea  dish 
over  the  flame.      Stir  with  a  glass  rod    and,  when 
reduced   to    fine    grayish-white    ash,    weigh    again. 
This  gives  the  mineral  matter,  or  ash. 

The  data  now  at  hand  are  as  follows: 

1.  The  weight  of  the  fresh  material. 

2.  The  weight  of  the  dry  solid. 


*  The  ash  may  be  obtained  directly  by  burning  a  piece  of 
fresh  fruit. 


18  NUMBER  WORK.  [September 

3.  The  weight  of  the  fluid — obtained  by  subtract- 
ing   weight    of   dry    solid   from    that   of   the    fresh 
material. 

4.  The  weight  of  the  ash. 

5.  The  weight  of  the  organic  matter — obtained 
by  subtracting  the  weight  of  the  ash  from  the  weight 
of  the  dry  solid. 

PROBLEMS. 

I.     WHOLE  NUMBERS — (Dry  Solid,  Fluid,  and  Fresh 
Material). 

1.  What  is  the  difference  between  the  weight 
of  the  fresh  fruit  and  that  of  the  dry  solid? 

2.  What  is  the  difference   between    the  weight 
of  the  fluid  and  that  of  the  dry  solid? 

3.  What  is  the  difference  between  the  weight  of 
the  fresh  material  and  that  of  the  fluid? 

4.  The  weight  of  the  fresh  material  is  how  many 
times  the  weight  of  the  dry  solid? 

5.  The  weight  of  the  fresh  material  is  how  many 
times  the  weight  of  the  fluid? 

6.  What  is  the  difference  between  the  weight  of 
the  dry   solid  obtained   from  ten  grams  of  apple 
and  that  obtained  from  the  same  amount  of  potato  ? 

7.  What  is  the  difference  between  the  weight  of 
the  fluid  in  ten  grams  of  apple  and  the  weight  of 
the  fluid  in  ten  grams  of  potato? 

8.  What  is  the  difference  between  the  dry  solid 
contained   in   ten  grams  of   turnip  and   the    dry 
solid  in  the  same  amount  of  sweet  potato?     What 
difference  between  the  amounts  of  fluid  in  the  two? 

9.  What  is  the  difference  between  the  weight  of 


September]  BOTANY.  19 

dry  solid  in  ten  grams  of  parsnip  and  that  in  the 
same  amount  of  a  beet? 

10.  What  is  the  difference  in  weight  between 
the  dry  solid  in  ten  grams  of  cucumber  and  the 
dry  solid  in  ten  grams  of  squash  ? 

II.     FRACTIONS — (Dry  Solid,  Fluid,  Fresh  Material, 
Organic  Matter,  and  Ask). 

1.  The  weight  of  the  dry  solid  is  what  part  of 
the  weight  of  the  fresh  material  ? 

2.  The  weight  of  the  fluid  is  what  part  of  the 
weight  of  the  fresh  material? 

3.  The  weight  of  the  ash  is  what  part  of  the 
weight  of  the  fresh  material? 

4.  The  weight  of  the  organic   matter  is   what 
part  of  the  weight  of  the  fresh  material  ? 

5.  The  weight  of  the  dry  solid  is  what  part   of 
the  weight  of  the  fluid  ? 

6.  The  weight  of  the  dry  solid  is  what  part  of 
the  weight  of  the  ash  ? 

7.  The  weight  of  the  dry  solid  is  what  part  of 
the  weight  of  the  organic  matter? 

8.  The  weight  of  the   fluid  is  what  part  of  the 
weight  of  the  dry  solid  ? 

9.  The  weight  of  the   fluid  is  what  part  of  the 
weight  of  the  ash  ? 

10.  The  weight  of  the  fluid  is  what  part  of  the 
weight  of  the  organic  matter? 

11.  The  weight  of  the  ash  is  what  part  of  the 
weight  of  the  fluid? 

12.  The  weight  of  the  ash  is  what  part  of  the 
weight  of  the  dry  solid? 


20  NUMBER  WORK.  [September 

13.  The  weight  of  the  ash  is  what  part  of  the 
weight  of  the  organic  matter? 

14.  The  weight  of  the   organic  matter  is  what 
part  of  the  weight  of  the  dry  solid? 

15.  The  weight  of  the  organic  matter  is  what 
part  of  the  weight  of  the  fluid? 

16.  The   weight  of  the  organic  matter  is  what 
part  of  the  weight  of  the  ash? 

17.  In  one  bushel  of  potatoes,  how  many  pounds 
of  fluid?     Of  ash?     Of  organic  matter?     Of  dry 
solid? 

18.  In  one  barrel  of  apples,  how  many  pounds 
of  fluid?     Of  ash?     Of  organic  matter?     Of  dry 
solid? 

19.  In    one    bushel     of    turnips,    how    many 
pounds  of  fluid?     Of  ash?     Of  organic   matter? 
Of  dry  solid? 

20.  In  one  bushel  of  beets,  how  many  pounds 
of  fluid?     Of  ash?     Of  organic  matter?     Of  dry 
solid? 

III.     RATIO. 

1.  What   is   the    ratio,   by   weight,   of  the  dry 
solid  to  the  fresh  material? 

2.  What  is  the  ratio,  by  weight,  of  the  fluid  to 
the  fresh  material? 

3.  What  is  the  ratio,  by  weight,  of  the  ash  to 
the  fresh  material? 

4..  What  is  the  ratio,  by  weight,  of  the  organic 
matter  to  the  fresh  material  ? 

5.  What  is  the  ratio,  by  weight,  of  the  dry 
solid  to  the  fluid? 


September]  BOTANY.  21 

6.  What  is  the   ratio,    by   weight,   of    the  dry 
solid  to  the  ash  ? 

7.  What  is  the  ratio,    by    weight,    of   the   dry 
solid  to  the  organic  matter? 

8.  What  is   the  ratio,  by  weight,  of    the   fluid 
to  the  ash? 

9.  What  is  the  ratio,  by  weight,   of    the  fluid 
to  the  organic  matter? 

10.  What  is  the  ratio,  by  weight,  of  the  ash  to 
the  organic  matter? 

11.  What  is  the  ratio,  by  weight,  of   the  fluid 
in  an  apple  to  that  in  a  turnip? 

12.  What  is  the  ratio,  by  weight,  of  the  ash  in 
an  apple  to  the  ash  in  a  turnip? 

13.  What  is  the  ratio,  by  weight,  of  the  organic 
matter  in  an  apple  to  that  in  a  potato? 

14.  What  is  the  ratio,  by  weight,  of  the  dry  solid 
in  a  potato  to  that  in  a  turnip? 

15.  What  is  the  ratio,  by  weight,  of  the  fluid  in 
a  parsnip  to  that  in  a  beet? 

16.  In  a  bushel  of  potatoes  how  much  fluid,  dry 
solid,  ash,  arid  organic  matter? 

17.  In  one  barrel  of  apples  how  much  fluid,  dry 
solid,  ash,  and  organic  matter? 

18.  In  a  bushel  of  turnips  how  much  fluid,  dry 
solid,  ash,  and  organic  matter? 

19.  In  a  bushel  of  parsnips  how  much  fluid,  dry 
solid,  ash,  and  organic  matter? 

20.  In  a  bushel  of  beets  how  much  fluid,  dry 
solid,  ash,  and  organic  matter? 

IV.  PERCENTAGE. 

1.  The  weight  of  the  dry  solid  is  what  per  cent 
of  the  weight  of  the  fresh  material  ? 


22  NUMBER  WORK.  [September 

2.  The  weight  of  the  fluid  is  what  per  cent  of 
the  weight  of  the  fresh  material? 

3.  The  weight  of  the  ash  is  what  per  cent  of  the 
weight  of  the  fresh  material  ? 

4.  The  weight  of  the  organic  matter  is  what  per 
cent  of  the  weight  of  the  fresh  material  ? 

5.  The  weight  of  the  dry  solid  is  what  per  cent 
of  the  weight  of  the  fluid?     The  fluid,  of  the  dry 
solid? 

6.  The  weight  of  the  dry  solid  is  what  per  cent 
of  the  weight  of  the  ash?     The   ash,  of  the  dry 
solid? 

7.  The  weight  of  the  dry  solid  is  what  per  cent 
of  the  weight  of  the  organic  matter?    The  organic 
matter,  of  the  dry  solid? 

8.  The  weight  of  the  fluid  is  what  per  cent  of 
the  weight  of  the  ash?     The  ash,  of  the  fluid? 

9.  The  weight  of  the  fluid  is  what  per  cent  of 
the  weight  of  the  organic  matter?     The  organic 
matter,  of  the  fluid? 

10.  The  weight  of  the  ash  is  what  per  cent  of 
the  weight  of  the  organic  matter?     The  organic 
matter,  of  the  ash  ? 

11.  The  amount  of  dry  solid  in  a  turnip  is  what 
per  cent,  by  weight,  of  that  in  an  apple? 

12.  The  amount  of  ash  in  a  turnip  is   what  per 
cent,  by  weight,  of  that  in  an  apple  ? 

13.  The   amount  of  organic  matter  in  a  turnip 
is  what  per  cent,  by  weight,  of  that  in  a  potato? 

14.  The  amount  of  ash  in  a  turnip  is  what  per 
cent,  by  weight,  of  that  in  a  potato? 


September]  BOTANY.  23 

15.  The  amount  of  fluid  in  a  parsnip  is  what  per 
cent,  by  weight,  of  the  amount  in  a  beet? 

16.  In  a  bushel  of  potatoes,  how  much  dry  solid, 
fluid,  ash,  and  organic  matter? 

17.  In  a  barrel  of  apples,  how  much  dry  solid, 
fluid,  ash,  and  organic  matter? 

18.  In  a  bushel  of  turnips,  how  much  dry  solid, 
fluid,  ash,  and  organic  matter? 

19  In  a  bushel  of  parsnips,  how  much  dry  solid, 
fluid,  ash,  and  organic  matter? 

20.  In  a  bushel  of  beets,  how  much  dry  solid, 
fluid,  ash,  and  organic  matter? 


PHYSICS. 


EVAPORATION  OF    LIQUIDS. 


In  order  to  use  the  following  problems,  it  is  neces- 
sary to  have  vessels,  similar  to  those  here  described, 
whose  dimensions  are  known.  They  can  be  made  by 
any  tinsmith  at  a  trifling  cost.  No.  I  is  cubical,  six 
centimeters  on  each  edge.  No.  II  is  rectangular, 
twelve  centimeters  long,  six  wide,  and  three  deep. 
No.  Ill  is  rectangular,  twelve  centimeters  long,  three 
wide,  and  six  deep.  No.  IV  is  rectangular,  six  centi- 
meters long,  three  wide,  and  twelve  deep.  No.  V  is 
right-triangular,  the  sides  adjacent  to  the  right  angle 
being  each  six  centimeters,  the  depth  being  twelve. 
It  will  be  seen  that  these  vessels  are  of  equal  capac- 
ity, but  that  the  surface  area  exposed  varies.  In 
setting  these  vessels  for  the  experiment,  it  is  best  to 
place  them  in  a  small  box  of  dry  saw-dust,  so  that 
the  variation  due  to  the  exposure  of  unequal  side 
areas  to  the  air  may  be,  practically,  eliminated. 

To  measure  the  amount  of  evaporation,  construct  a 
small  frame  to  stand  over  each  vessel.  Through  a 
cross-piece  in  this  frame  directly  over  the  vessel  pass 
a  steel  knitting-needle,  the  lower  end  of  which  must 
be  filed  to  a  very  sharp  point.  To  the  upper  side  of 
the  cross-piece,  just  behind  the  needle,  fasten  a  small 
strip  of  wood  about  two  centimeters  wide  and  four 
high ;  on  the  face  of  this,  next  to  the  needle,  tack  a 

24 


September]  PHYSICS.  25 

piece  of  thin  copper,  brass,  or  tin  and  rule  upon  it 
horizontal  lines,  one  millimeter  apart.  Heat  the 
upper  end  of  the  needle  and  bend  the  tip  of  it  at 
right  angles  so  that  it  will  pass  over  the  face  of  the 
scale. 

To  take  the  observation,  fill  the  vessels  nearly  to  the 
top  with  the  liquid  to  be  studied,  and  move  the  needle 
down  until  the  point  comes  in  contact  with  the  sur- 
face. The  surface  may  be  slightly  varied  by  means 
of  a  dropping  tube  so  that  the  upper  end  of  the 
needle  will  rest  exactly  on  one  of  the  lines  of  the 
scale  when  the  point  is  in  contact  with  the  liquid. 
Place  the  vessels,  under  whatever  conditions  desired, 
for  a  definite  time;  then,  push  the  needle  down 
until  the  point  again  comes  in  contact  with  the 
surface,  and  read  on  the.  scale  the  number  of  milli- 
meters passed  over  by  the  upper  end.  This  will  give 
the  depth  evaporated,  and  the  volume  may  be  calcu- 
lated. In  determining  the  point  of  contact  of  the 
needle  and  liquid  it  is  best  to  place  the  eye  so  that 
the  reflection  of  the  needle  may  be  seen  rising  to 
meet  the  descending  point;  the  surface  is  at  the  exact 
point  of  the  meeting  of  the  two.  All  the  vessels  may 
be  placed  under  the  same  conditions,  or  one  may  be 
placed  under  different  conditions  at  different  times; 
or  all  the  vessels  may  be  so  used.  These  observa- 
tions render  it  necessary  for  the  pupils  to  calculate 
areas  and  volumes  that  the  subject  of  evaporation 
may  be  definitely  understood.  It  is,  therefore, 
directly  a  study  of  evaporation,  which  is  a  study  of 
heat  and  atmospheric  conditions  and,  incidentally,  a 
practical  study  of  the  subject  of  mensuration. 


26  NUMBER  WORK.  [September 

PROBLEMS. 

I.     WHOLE  NUMBERS. — A.    Conditions  and  time  the 
same  for  all  the  vessels. 

1.  What   is  the  volume  evaporated  from  No.  I? 
What  is  the  average  per  hour? 

2.  What  is  the  volume  evaporated  from  No.  II  ? 
Average  per  hour? 

3.  What  is  the  volume  evaporated  from  No.  III? 
Hourly  average? 

4.  What  is  the  volume  evaporated  from  No.  IV  ? 
Hourly  average? 

5.  What  is  the  volume  evaporated  from  No.  V  ? 
Hourly  average?     Measure  off  in  a  graduate  the 
above  amounts  that  the  pupils  may  become  familiar 
with  the  different  volumes. 

6.  Which  evaporated  the  more,  and  how  much, 
No.  I  or  No.  II? 

7.  Which  has  the  larger  surface,  and  how  much, 
No.  I  or  No.  II? 

8.  Which  evaporated  the  more,  and  how  much, 
No.  I  or  No.  IV? 

9.  Which  has  the   greater   area   exposed,   and 
how  much,  No.  I  or  No.  IV? 

10.  Which  evaporated  the  larger  volume,  and 
how  much,  No.  I  or  No.  V? 

11.  Which  has  the  larger  area  exposed,  and  how 
much,  No.  I  or  No.  V? 

12.  Which  evaporated  the  larger  volume,  and 
how  much,  No.  II  or  No.  III? 

13.  Which  has  the  larger  area  exposed,  and  how 
much,  No.  II  or  No.  III? 

14.  Which  evaporated  the  more,  and  how  much, 
No.  II  or  No.  IV? 


September]  PHYSICS.  27 

15.  Which  has  the  larger  area  exposed,  and  how 
much,  No.  II  or  No.  IV? 

16.  Which  evaporated  the  more,  and  how  much, 
No.  IV  or  No.  V? 

17.  Which  has  the  larger  surface  exposed,  and 
how  much,  No.  IV  or  No.  V? 

B.    Different  conditions. 

18.  Which    is    greater,     and    how     much,    the 
hourly  average  of  the  vessels  when  inside  a  room 
or  on  the  outside  of  the  window  sill  ? 

19.  Which  is  greater,  and  how  much,  the  hourly 
average,  when  the  vessels  are  in  a  window,  with 
the  window  open,  or  with  it  closed? 

20.  Which  is  greater,  the  hourly  average  on  a 
rainy  day  or  a  clear  day  ? 

21.  Which  is  greater,  and  how  much,  the  hourly 
average  with  the   vessels  in  a  closed  cupboard  or 
in  an  open  room  ? 

22.  Which  is  greater,  and  how  much,  the  evap- 
oration  with    the   vessels  in    sunshine    or  in    the 
shade  ? 

II.     FRACTIONS. — A.  Conditions  and  time  the  same 
for  all  the  vessels. 

1.  The  volume  evaporated    from  No.   I  equals 
what  part  of  that  evaporated  from  No.  II? 

2.  The  area  exposed  in  No.  I  equals   what  part 
of  that  exposed  in  No.  II? 

3.  The  amount  evaporated  from  No.   I    equals 
what  part  of  that  evaporated  from  No.  Ill  ? 

4.  The   area  exposed  in  No.  I  equals  what  part 
of  that  exposed  in  No   III? 


28  NUMBER  WORK.  [September 

5.  The   amount   evaporated  from   No.  I  equals 
what  part  of   that  evaporated  from  No.  IV  ? 

6.  The  area  exposed  in  No.  I  equals  what  part 
of  that  exposed  in  No.  IV? 

7.  The  amount  evaporated  from  No.   I  equals 
what  part  of  that  evaporated  from  No.  V? 

8.  The  area  exposed  in  No.  I  equals  what  part 
of  that  exposed  in  No.  V  ? 

9.  The   amount   evaporated  from  No.  II  equals 
what  part  of  that  evaporated  from  No.  III? 

10.  The    area    exposed  in  No.  II    equals  what 
.part  of  that  exposed  in  No.  III? 

11.  The  amount  evaporated  from  No.  II  equals 
what  part  of  that  evaporated  from  No.  IV? 

12.  The   area  exposed   in  No.    II  equals    what 
part  of  that  exposed  in  No.  IV? 

13.  The  amount  evaporated  from  No.   II  equals 
what  part  of  that  evaporated  from  No.  V? 

14.  The  area  exposed  in  No.  II  equals  what  part 
of  that  exposed  in  No.  V  ? 

15.  The  amount  evaporated  from  No.  IV  equals 
what  part  of  that  evaporated  by  No.  V  ? 

16.  The  area   exposed  in   No.  IV   equals  what 
part  of  that  exposed  in  No.  V? 

B.  Different  conditions. 

17.  The  hourly  average  evaporated  with  the  ves- 
sels in  a  closed  cupboard  equals  what  part  of  the 
average  when  they  are  in  a  room? 

18.  The   hourly  average  with  the  vessels  near 
a  closed  window  equals  what  part  of  the  average 
when  the  window  is  open? 

19.  The   hourly    average  on  a  dry   day  equals 
what  part  of  that  on  a  rainy  day  ? 


Septen  \  1  ><  M-  |  PH  YSICS.  29 

20.  The   hourly  average  with  the  vessels  in  the 
sunshine  equals  what  part  of  that  when  they  are 
in  the  shade  ? 

21.  The  hourly  average  with  the  vessels  outdoors 
equals  what  part  of  that  when  they  are  indoors? 

III.     RATIO. — A.  Conditions  and  time  the  same  for 
all  the  vessels. 

1.  What  is  the   ratio  of  the  volume  evaporated 
from  No.  I  to  that  evaporated  from  No.  II? 

2.  What  is  the  ratio  of  the  area  exposed  in  No. 
I  to  that  exposed  in  No.  II  ? 

3.  What  is  the  ratio  of  the  volume  evaporated 
from  No.  I  to  that  evaporated  from  No.  III? 

4.  What  is  the  ratio  of  the  area  exposed  in  No. 
I  to  that  exposed  in  No.  Ill  ? 

5.  What  is  the  ratio  of  the  volume  evaporated 
from  No.  I  to  that  evaporated  from  No,  IV  ? 

6.  What  is  the  ratio  of  the  area  exposed  in  No. 
I  to  that  exposed  in  No.  IY? 

7.  What  is  the  ratio  of  the  amount  evaporated 
from  No.  I  to  that  evaporated  from  No.  V? 

8.  What  is  the  ratio  of  the  area  exposed  in  No. 

I  to  that  exposed  in  No.  V  ? 

9.  What  is  the  ratio  of  the   amount  evaporated 
from  No.  II  to  that  evaporated  from  No.  Ill  ? 

10.  What  is  the  ratio  of  the  area  exposed  in  No. 

II  to  that  exposed  in  No.  Ill  ? 

11.  What  is  the  ratio  of  the  amount  evaporated 
from  No.  II  to  that  evaporated  from  No.  IV  ? 

12.  What  is  the  ratio  of  the   area  exposed  in 
No.  II  to  that  exposed  in  No.  IV  ? 


30  NUMBER  WORK.  [September 

13.  What  is  the  ratio  of  the  amount  evaporated 
from  No.  II  to  that  evaporated  from  No.  V? 

14.  What  is  the  ratio  of   the   area  exposed  in 
No.  II  to  that  exposed  in  No.  V  ? 

15.  What  is  the  ratio  of  the  amount  evaporated 
from  No.  IV  to  that  evaporated  from  No.  V? 

16.  What  is  the  ratio  of  the  area   exposed  in 
No.  IV  to  that  exposed  in  No.  V? 

£.  Different  conditions. 

17.  What  is  the  ratio  of  the  hourly  average  of 
evaporation  when  the  vessels  are  in  a  closed  cup- 
board to  that  when  they  are  in  an  open  room? 

18.  What  is  the  ratio  of  the  hourly  average  of 
evaporation   when  the  vessels  are  near   a  closed 
window  to  that  when  the  window  is  open  ? 

19.  What  is  the  ratio  of  the  hourly  average  of 
evaporation  on  a  rainy  day  to  that  on  a  clear  day  ? 

20.  What  is  the  ratio  of  the  hourly  average  of 
evaporation  when  the  vessels  are  in  the  sunshine 
to  that  when  they  are  in  the  shade? 

21.  What  is  the  ratio  of  the  hourly  average  of 
evaporation  when  the  vessels  are  outdoors  to  that 
when  the  vessels  are  indoors  ? 

IV.     PERCENTAGE. — A.     Conditions   and   time    the 
same  for  all  the  vessels. 

1.  The  volume   evaporated  from  No.  I    equals 
what  per  cent  of  that  evaporated  from  No.  II  ? 

2.  The  area  exposed  in  No.  I  equals  what  per 
cent  of  that  exposed  in  No.  II  ? 

3.  The  volume   evaporated   from  No.   I   equals 
what  per  cent  of  that  evaporated  from  No.  III? 


September]  PHYSICS.  31 

4.  The  area  exposed  in  No.  I  equals  what  per 
c»M it  of  that  exposed  in  No.  III? 

5.  The    volume    evaporated  from  No.  I  equals 
what  per  cent  of  that  evaporated  from  No.  IV  ? 

6.  The  area  exposed  in  No.  I  equals  what  per 
cent  of  that  exposed  in  No.  IV  ? 

7.  The  volume  evaporated  from  No.  I   equals 
what  per  cent  of  that  evaporated  from  No.  V  ? 

8.  The  area  exposed  in  No.  I  equals  what  per 
cent  of  that  exposed  in  No.  V  ? 

9.  The  volume  evaporated  from  No.  II  equals 
what  per  cent  of  that  evaporated  from  No.  Ill  ? 

10.  The  area  exposed  in  No.  II  equals  what  per 
cent  of  that  exposed  in  No.  Ill  ? 

11.  The  volume  evaporated  from  No.  II  equals 
what  per  cent  of  that  evaporated  from  No.  IV  ? 

12.  The  area  exposed  in  No.  II  equals  what  per 
cent  of  that  exposed  in  No.  IV  ? 

13.  The  volume  evaporated  from  No.  II  equals 
what  per  cent  of  that  evaporated  from  No.  V  ? 

14.  The  area  exposed  in  No.  II  equals  what  per 
cent  of  that  exposed  in  No.  V  ? 

15.  The  amount  evaporated  from  No.  IV  equals 
what  per  cent  of  that  evaporated  from  No.  V  ? 

16.  The  area  exposed  in  No.   IV  equals  what 
per  cent  of  that  exposed  in  No.  V? 

B.  Different  conditions. 

17.  The    hourly    average    evaporated  with    the 
vessels  in  a  closed  cupboard  equals  what  per  cent 
of  that  evaporated  when  they  are  in  a  closed  room? 

18.  The  hourly  average    evaporated   when  the 
vessels  are  near  a  closed  window  equals  what  per 
cent  of  that  when  the  window  is  open? 


32  NUMBER  WORK.  [September 

19:  The  hourly  average  evaporated  on  a  dry 
day  equals  what  per  cent  of  that  evaporated  on 
a  wet  one? 

20.  The    hourly  average   evaporated   when  the 
vessels   are  in  the  sunshine  equals  what  per  cent 
of  that  when  they  are  in  the  shade? 

21.  The  hourly  average   evaporated    when   the 
vessels  are  outdoors  equals  what  per  cent  of  that 
when  they  are  indoors? 


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METEOROLOGY. 


In  order  to  gather  the  data  required  for  the  fol- 
lowing problems,  it  is  necessary  that  the  pupils  keep 
a  daily  weather  record.*  A  blank  form,  sufficient  for 
a  week  s  record,  devised  for  the  public  schools,  is 
here  copied  from  NATURE  STUDY  FOR  THE  COMMON 
SCHOOLS,  in  which  book  its  use  is  more  fully 
described.  As  soon  as  the  pupils  can  do  the  work, 
each  should  be  provided  with  a  sheet  large  enough 
to  contain  a  month's  record. 

The  teacher  should  apply  to  the  nearest  Weather 
Bureau  Office  for  the  daily  weather  maps,  and  they, 
together  with  a  valuable  monthly  summary,  will  be 
sent  free  of  charge.  With  these  the  pupils'  obser- 
vations may  be  supplemented  and  corrected. 

With  small  children,  the  record  may  be  kept  on 
the  blackboard  by  the  teacher,  and  only  such  points 
noticed  as  the  children  are  able  to  give  themselves, 
such  as  direction  of  wind,  clouds,  etc. 
I.     WHOLE  NUMBERS. 

A.     Temperature. 

1.  What  is  the  difference  between  the  lowest 

and  the  highest  temperature  for  September? 

*A  Science  Record,  devised  by  the  author,  contains  a 
sufficient  number  of  blank  forms  for  a  year's  work.  It  is  also 
provided  with  blank  pages  for  writing,  and  drawings,  and  a 
mineralogical  record. 

34 


September]  METEOROLOGY.  35 

2.  What  is   the    average    temperature    for    the 
month  ? 

3.  What  is  the  average  temperature  for  the  first 
week?     The  second?     The  third?     The   fourth? 

4.  What  is  the  greatest  difference  in  the  aver- 
age   temperature  between  any  two   weeks   of  the 
month  ? 

B*     Barometer. 

5.  What  is  the  average  hight  of  the  barometer 
for  September? 

6.  What  is  the   difference  between  the   lowest 
and  the  highest  reading  for  the  month  ? 

7.  What  is  the  average  hight  for  the  first  week  ? 
The  second  ?     The  third  ?     The  fourth  ? 

8.  WThat  is  the  greatest  difference  between  the 
average  hights  for  any  two  weeks? 

C.  Rainy ,  Cloudy -,  and  Clear  Days. 

9.  How  many   rainy    days  during   September? 
Cloudy  days?     Cloudy   days  without  rain?  Clear 
days? 

10.  What  is  the  difference  between  the  number 
of  rainy  days  and  the  number  of  cloudy  days? 

11.  What  is  the  difference  between  the  number 
of  rainy  days  and  the  number  of  clear  days  ? 

12.  What  is  the  difference  between  the  number 
of  cloudy  days  and  the  number  of  clear  days? 

13.  At    the  September    rate,   how  many  rainy 
days  would  there  be  in  a  year  ?     How  many  cloudy 
days?     How  many  clear  days? 

D.  Rainfall. 

14.  What  is  the  total  rainfall  for  the  month  ? 


36  NUMBER  WORK.  [September 

15.  What  is  the   average  rainfall  for  each  day 
of  the  month? 

16.  What  is  the  average  rainfall  for  each  cloudy 
day  in  the  month? 

17.  What  is  the  average  rainfall  for  each  rainy 
day  in  the  month  ? 

18.  At  the  September  rate,  what  would  be  the 
total  rainfall  for  a  year? 

E.     Dew,  Frost,  and  Fogs. 

19.  How  many  mornings  during  the  month  were 
with  dew? 

20.  Which   is   the  greater,  and  how   much,  the 
number  of  mornings  with  dew  or  the  number  with 
frost? 

21.  On  how   many   mornings  were  fogs  noted? 

22.  What  is  the  difference  between  the  number 
of  clear  mornings  and  the  number  of  foggy  morn- 
ings ?     With  dew,'  and  without  dew  ? 

II.     FRACTIONS. 

A.  Temperature. 

1.  The  lowest  reading  of   the  thermometer  for 
the  month  of  September  is  what  part  of  the  highest  ? 

2.  The  average  reading  of  the  thermometer  for 
the  first  week  is  what  part  of  that  for  the  month  ? 
For  the  second  week  ?     For  the  third  week  ?     For 
the  fourth  week? 

3.  The  average  reading  of  the  thermometer  for 
the  first  week  is  what  part  of  that  for  the  second? 
The  third  ?    The  fourth  ? 

B.  Barometer. 

4.  The   average    hight    of    the    barometer   for 


September]  METEOROLOGY.  37 

September  is  what  part  of  the  highest   reading? 
The  lowest? 

5.  The  average  hight  for  the  first  week  is  what 
part  of   that  for  the    second?     The    third9     The 
fourth  ? 

6.  The  average   hight  during  the  rainy  days  is 
what  part  of   that  for  the  entire  month  ? 

7.  The    average    hight    for    the   rainy   days    is 
what  part  of  that  for  the  cloudy  days? 

8.  The    average   hight   for    the   rainy   days    is 
what  part    of   that  for  the  cloudy  days  that  were 
without  rain? 

9.  The    average    hight  for  the    rainy    days  is 
what  part  of   that  for  the  clear  days? 

C.     Itainy,  Cloudy,  and  Clear  Days. 

10.  The  number  of  rainy  days  is  what  part  of 
the  entire  month? 

11.  The  number  of  rainy  days  equals  what  part 
of  the  number  of  cloudy  days  ? 

12.  The  number  of  rainy  days  equals  what  part 
of  the  number  of  clear  days  ? 

13.  The  number  of  cloudy  days  is  what  part  of 
the  entire  month? 

14.  The  number  of  cloudy  days  without  rain  is 
what  part  of  the  entire  month  ? 

15.  The  number  of  clear  days  is  what  part  of 
the  entire  month  ? 

16.  What  wind  accompanied  the  greater  part  of 
the  number  of  cloudy  days? 

17.  What  wind  accompanied  the  greater    part 
of  the  number  of  clear  days? 


38  NUMBER  WORK.  [September 

D.  Rainfall. 

18.  What  part  of  the  total  rainfall  fell  the  first 
week  ?     The  second  ?     The  third  ?     The  fourth  ? 

19.  The  daily  average  rainfall  for  the  rainy  days 
equals  what  part  of  that  for  the  entire  month  ? 

20.  The   daily   average   rainfall    for   the    rainy 
days  equals  what  part  of  that  for  the  total  number 
of  cloudy  days? 

21.  The  daily  average   rainfall  for  the  days  on 
which  the  prevailing  wind  blew  equals  what  part 
of  that  for  the  other  days  of  the  mouth  ? 

E.  Dew,  Frost,  Fogs. 

22.  The  dewy  mornings  are   what   part  of  the 
entire  month? 

23.  The  mornings  with   frost  are  what  part  of 
the  entire  month  ? 

24.  The  mornings  with  fogs  are  what  part  of 
the  entire  month? 

III.     RATIO. 

A.     Temperature. 

1.  What  is  the  ratio  of  the  lowest  reading  of 
the  -thermometer  to  the  highest  in  September? 

2.  What  is  the  ratio  of  the  average  reading  of 
the  thermometer  of  the  first  week  to  that  of  the 
second?     Of  the   second   to    the    third?     Of  the 
third  to  the  fourth  ? 

3.  What  is  the  ratio  of  the  average  reading  of 
the  thermometer  of  the  first  week  to  the  monthly 
average?     Of   the   second    week?     Of    the    third 
week  ?     Of  the  fourth  week  ? 


September]  M  K  TEOROLOG  Y.  30 

B.  Barometer. 

4.  What    is    the    ratio    of    the    lowest    to    the 
highest  reading  for  the  month  ? 

5.  What  is  the  ratio  of  the  average  reading  for 
the  rainy  days  to  that  for  the  clear  days  ? 

().  What  is  the  ratio  of   the  average  reading  for 
the  cloudy  days  to  that  for  the  clear  days? 

7.  What  is  the  ratio  of  the  average  reading  on 
the  rainy  days  to  that  of   the  cloudy  days  without 
rain  ? 

8.  What  is  the  ratio  of  the  average  reading  on 
the  cloudy  days  without  rain  to  that  for  the  clear 
days? 

C.  Rainy,  Cloudy,  and  Clear  Days. 

9.  What  is  the  ratio  of  the  number   of  rainy 
days  to  the  number  of  clear  days  ? 

10.  What  is  the  ratio  of  the  number  of  rainy 
days  to  the  number  of  cloudy  days? 

11.  What  is  the  ratio  of  the  number  of  rainy 
days  to  the  number  of  cloudy  days  without  rain? 

12.  What  is  the  ratio  of  the  number  of  cloudy 
days  to  the  number  of  clear  days? 

13.  What  is  the  ratio  of  the  number  of  cloudy 
days  without  rain  to  the  number  of  clear  days? 

D.  Rainfall. 

14.  What  is  the  ratio  of  the  rainfall  of  the  first 
week  to  the  total  for  the  month  ?     Of  the  second 
week?     Of  the  third  week?     Of  the  fourth? 

15.  The  daily  average  rainfall  for  the  rainy  days 
bears  what  ratio  to  the  daily  average  for  the  month? 


40  NUMBER  WORK.  [September 

16.  The  daily  average  for  the  rainy  days  bears 
what  ratio  to  the  daily  average  for  the  cloudy  days  ? 
E.     Dew,  Frost,  Fog. 

17.  What  is  the  ratio  of  the  dewy  mornings  to 
those  with  frost  ? 

18.  What  is  the  ratio  of  the  number  of  foggy 
mornings  to  the  number  without  fogs? 

IV.     PERCENTAGE. 

A .  Temperature. 

1.  The  lowest  reading  of  the  thermometer  for 
the  month    is  what  per  cent  of  the  highest  ? 

2.  The  average  reading  of  the  thermometer  for 
the  first   week  is   what  per  cent  of  that  for   the 
month  ?  Of  the  second  week  ?    Of  the  third  week  ? 
Of  the  fourth  week? 

3.  The  average  reading  of  the  thermometer  for 
the  rainy  days  is   what  per  cent  of  that  for  the 
clear  days? 

4.  The  average  reading  of    the  thermometer  for. 
the  cloudy  days  is  what  per  cent  of  that  for  the 
clear  days? 

5.  The  average  reading  of  the  thermometer  for 
the  rainy  days  is  what   per  cent  of  that  for  the 
cloudy    days  without  rain? 

B.  Barometer. 

6.  The  lowest  barometric  reading  for  the  month 
is  what  per  cent  of  the  highest  ? 

7.  The  average  hight  of   the  barometer  for  the 
first  week  is  what  per  cent  of  that  for  the  month  ? 
Of  the  second?     Of  the  third?     Of  the  fourth? 


September]  METEOROLOGY.  41 

8.  The  average  hight  of  the  barometer  during 
the  rainy  days  is  what  per  cent  of  that  during  the 
clear  days? 

9.  The  average  hight  of  the  barometer  during 
the  cloudy  days  is  what  per  cent  of  that  during 
the  clear  days? 

10.  The  average  hight  of  the  barometer  during 
the  rainy  days  is  what  per  cent  of  that  during  the 
cloudy  days  without  rain? 

11.  The  average  hight  of  the  barometer  for  the 
days  on  which  the  prevailing  wind  blew  is  what 
per  cent  of  that  for  the  other  days  of  the  month  ? 

C.  Rainy,  Cloudy,  and  Clear  Days. 

12.  The  number  of  rainy  days  is  what  per  cent 
of  the  entire  month? 

13.  The   number  of   cloudy  days  is  what    per 
cent  of  the  entire  month? 

14.  The  number  of  clear  days  is  what  per  cent 
of  the  entire  month? 

15.  The  number  of  rainy  days  is  what  per  cent 
of  the  number  of  cloudy  days  ? 

16.  The  number  of  rainy  days  equals  what  per 
cent  of  the  number  of  clear  days? 

17.  The  number  of  cloudy  days  equals  what  per 
cent  of  the  number  of  clear  days? 

18.  The  rainy  days  with  the  wind  in  the  pre- 
vailing direction   for  the  month  equals  what  per 
cent    of    the    number   with    the    wind    in    other 
directions  ? 

D.  Rainfall. 

19.  The    average    daily  rainfall    for   the   rainy 
days  is  what  per  cent  of  that  for  the  entire  month  ? 


42  NUMBER  WORK.  [September 

20 .  The  average  rainfall  for  the  rainy  days  is 
what  per  cent  of  that  for  ttie  cloudy  days? 

21.  The  rainfall  of  the  first  week  is  what  per 
cent  of  that  for  the  entire  month  ?     Of  the  second 
week?     Of  the  third  week?     Of  the  fourth  week? 

22.  The   rainfall  on    the  days  when    the  wind 
blew  in  the  prevailing  direction  is  what  per  cent  of 
that  which  fell  on  the  other  days  of  the  month? 

E.     Dew,  Frost,  Fogs. 

'23.  The  dewy  mornings  are  what  per  cent  of 
the  entire  month? 

24.  The  frosty  mornings  are  what  per  cent  of 
the  entire  month  ? 

25.  The  days  with   fogs  are  what    per  cent  of 
the  entire  month? 


ASTRONOMY. 


THE  MUTUAL  RELATIONS  OF  THE  EARTH 
AND  SUN. 

It  is  a  fact,  easily  within  the  comprehension  of 
very  young  pupils,  that  the  condition  of  things,  as 
we  now  find  them  on  the  earth,  is  absolutely  depend- 
ent upon  the  particular  relation  which  now  exists 
between  the  earth  and  sun.  It  follows,  therefore, 
that  a  proper  study  and  knowledge  of  this  relation 
is  one  of  fundamental  importance,  if  the  phenom- 
ena of  climate  and  life  distribution  are  to  be  at 
all  understood.  In  this  study,  it  is  a  singular 
fact  that,  while  it  is  possible  for  pupils  of  public - 
school  age,  wherever  they  may  be  situated,  to  make 
a  large  number  of  observations,  it  is  true  that  all,  or 
nearly  all,  of  these  observations  will  lead  them 
directly  away  from  the  truth  regarding  the  earth 
and  the  sun.  The  earth  appears  to  be  flat,  but  it 
is  really  round,  like  a  ball;  it  seems  to  be  stationary, 
but  it  is  in  inconceivably  rapid  motion — in  fact,  it 
has  several  motions.  The  sun  appears  to  sweep 
through  a  great  arc  in  the  heavens  daily,  and  to 
rise  toward  the  zenith,  and  then  sink  toward  the 
horizon,  in  the  course  of  a  year,  moving  on  a  spiral 
line;  relatively,  though,  it  is  stationary.  The  sun 
seems  to  be  much  smaller  than  the  earth,  but  it 

43 


44  NUMBER  WORK.  [September 

really  is  vastly  larger.  Unaided,  it  is  impossible  for 
the  pupil  to  reach  the  truth  with  any  means  that  he 
is  able  to  employ,  and  it  is  necessary,  therefore,  that 
the  teacher  place  before  him,  in  proper  order,  a 
series"  of  statements  of  certain  leading  facts  that 
have  been  determined  by  prolonged  observation  and 
accurate  measurements.  By  this  means,  the  observa- 
tions of  the  pupils  will  gradually  assume  a  proper 
significance  to  them.  In  their  study  of  mathemat- 
ical geography,  it  often  happens  that  pupils  do  not 
get  a  proper  concept  of  the  size,  distances,  and  rates 
of  motion,  actual  or  relative,  of  the  heavenly  bodies. 
While  it  is  not  possible  to  approach  an  adequate 
concept  of  these,  as  they  actually  are,  by  proper 
means,  an  intelligent  notion  may  be  given  of  the 
relations  that  exist. 

A  few  suggestions  are  given  to  indicate  to  the 
teacher  how  the  observations  of  the  pupils  may  be 
utilized  in  this  study. 

I.     CONCERNING  THE  EARTH'S  SHAPE. 

1.  The  earth  appears  to  be  flat;  if  it  were  really 
flat,  what  would  be  the  fact  concerning  sunrise  to 
the  inhabitants   on  different  parts  of  the   earth's 
surface  ? 

2.  How   would  sunset  appear  under  the  same 
condition  ? 

3  The  sun  appears  to  be  smaller  than  the  earth ; 
if  it  were  really  so  and  if  the  earth  were  flat,  what 
would  be  the  facts  concerning  the  forenoon,  noon, 
and  afternoon  on  different  parts  of  the  earth's 
surface  ? 


September]  ASTRONOMY.  45 

(a)  Statement.     The    sun    is  approximately    eight 
hundred  sixty   thousand  miles  in  diameter;  the 
diameter  of  the  earth  is  eight  thousand  miles. 

4.  The  diameter  of  the  earth  bears  what  ratio 

to  that  of  the  sun? 

5.  If  the  diameter  of  the  sun   appears  to  you 
to    be    two   feet    (teacher  will  take    the    average 
apparent   diameter   as  given  by  the  pupils)  what 
would  the  diameter  of  the  earth  appear  to  be  if 
you  were  on  the  sun? 

6.  Suppose  you   represent  the  diameter  of  the 
earth  by  a  line  one   inch  long,  by  what  length  of 
line  must  you   represent  the  diameter  of  the  sun? 

(b)  Statement.     The  distance  from  the  earth  to  the 
sun  is  ninety -three  million  miles. 

7.  How  far  apart  must  the  two  lines  given  in 
(6)  be  placed  that  the  distance  between  them  may 
bear  a  proper  relation  to  the  respective  diameters 
of  the  earth  and  the  sun? 

8.  The  sun  being  so  much  larger  than  the  earth, 
if  the  latter  were  flat,  what  would  be    the  facts 
about  the  forenoon,  noon,  and  the   afternoon  on 
different  parts  of  the  earth? 

9.  What  facts  do  you   know  to  actually  exist 
concerning  sunrise,  forenoon,  noon,  afternoon,  and 
sunset  on  different  parts  of  the  earth  ? 

10.  Telegraphic  communication   now   makes  it 
possible  for  us  to  read  in  the  daily  papers  of  an  event 
that  has  taken  place  in  Europe  on  the  same  day, 
but,  according  to  our  clocks,  at  an  earlier  hour  than 
that  at  which  the  event  occurred.    That  is,  we  may 
read  at  eight  or  nine  o'clock  A.  M.  about  what  is  said 


46  NUMBER  WORK.  [September 

to  have  occurred  at  twelve,  noon.  Clocks  indicate 
indirectly  the  position  of  the  sun  in  the  heavens, 
and  it  follows,  from  the  foregoing,  that  when  the 
sun  is  at  the  zenith  at  one  place  it  is  much  nearer 
the  horizon  at  another.  The  newspaper  reports 
show,  respecting  two  places,  one  west  the  other- 
east,  that  at  the  same  moment  the  sun  will  be 
nearer  the  eastern  horizon  at  the  former  place 
than  the  latter;  also,  that  it  is  possible  for  two 
persons  to  be  so  situated  that  the  one  in  the  east 
may  see  the  sun  in  the  zenith  while  the  other  may 
see  it  at  the  same  time  on  his  eastern  horizon. 

11.  What  is  the  relation  to  each  other  of  the 
lines  of  vision  of  the  two  persons  who  thus  see  the 
sun,  one  in  the  zenith,  one  on  the  horizon? 

12.  What  is  the  supposition  that  can  be  made 
that  will  explain  the  fact  ?     Can  it  be  explained  by 
more  than  one  supposition? 

13.  When  one   ascends  an  elevation,  how  does 
the  horizon  line  change?     Can  this  be  explained 
by  more  than  one  supposition? 

14.  What  conclusion   can  be  drawn   from    the 
foregoing  study  respecting  the  shape  of  the  earth? 

II.     CONCERNING  THE  SLANT  OF   THE  SUN'S   RAYS. 

1.  What  is  the  relation,  to  each  other,  of   the 
shortest  rays  of    light  and  heat  that  fall  from  the 
sun  u  pon  the  lighted  area  of  the  earth  ? 

2.  If  the  earth  were  flat,  since  the  sun  is  larger 
than  the   earth,  upon  what   would  the   degree  of 
slant  of  the  rays  depend? 

3.  If  the  earth  were  flat,  what  would  be  the 


September]  ASTRONOMY.  47 

relation  between  the  degrees  of  slant  on  different 
parts  of  the  earth? 

4.  From   what  was  learned  under  I,  Topic  10, 
what  must  be  true  concerning  the  degree  of  slant  on 
different  parts  of  the  earth  within  the  lighted  area  ? 

5.  What  is  the  relation,  to  the  earth,  of  the  rays 
that  strike  the   central  point  of  the  lighted  area? 

6.  What  is  the  relation,  fo  the  earth,  of  the  rays 
that  strike  the  extreme  border  of  the  lighted  area? 

7.  What  supposition   respecting  the  surface  of 
the  earth  will  account  for  the  facts  about  the  slant 
of  the  rays? 

III.     CONCERNING  THE  EARTH'S  MOTIONS. 
A.     Rotation. 

1.  Supposing  the  earth  to  be  stationary,  as  it 
seems  to  be,  what  movement  must  the  sun  perform 
in  order  to  produce  day  and  night? 

2.  The  sun  being  distant  ninety-three  million 
miles,  how  far  would  it  have  to  travel  to  produce  a 
day  and  a  night? 

3.  In  what  time  would  the  sun  have  to  travel 
the  distance  necessary    to    produce  a  day   and  a 
night?     How  far  in  one  hour?     How  far  in  one 
second  ? 

(c)  /Statement.     The    sun,   in  its    relation    to   the 
earth,  may  be  regarded  as  being  stationary. 

4.  What   supposition  can   you  make  that  will 
explain  the  occurrence  of  day  and  night? 

5.  The    earth's    circumference    is    twenty -five 
thousand  miles;   how  far   must  a  given  point  on 
the  equator  move  during  the  time  of  one  day  and 
night?     How  far  in  one  hour?     In  one  second? 


*"norT  \7ir-DeTffiV 


48  NUMBER  WORK.  [September 

6.  If  the  earth  were  stationary,  from    appear- 
ances, what  would  be  the  truth  respecting  not  only 
the  sun  but  all  the  stars  near  and  remote  ? 

7.  Which  supposition  explains  the  appearances 
in  the  simpler  manner? 

B.     Revolution. 

1.  The  sun  being  regarded  as  stationary,  what 
movements  of  the   earth   can  you  imagine  which 
will  give  to  the  sun  its  apparent  movement  on  the 
meridian  in  the  course  of  a  year? 

2.  Imagine  a  tipping  of  the  north  pole  toward 
the  sun  during  six  months   and  a   tipping  away 
from   it  during  the   remaining  six  months;  what 
would  be  the  apparent  motion  of  the  sun  during 
that  time? 

3.  Imagine  the  earth  with  &  pivotal  motion  on 
the  south  pole — a  wabbling  motion  like  that  of  a 
dying  top;  how  would  the  sun  appear  to  move? 
(d)  Statement.     The  north  star  may  be  regarded  as 

a  fixed  star. 

4.  If  the  earth  tipped  or  wabbled,  what  would 
be  apparently  true  of  the  north  star  in  each  case? 

5.  With  these  facts  in  mind,  what  possible  sup- 
position can  be  made  respecting  the  earth's  motion 
which   will  account  for  the  apparent  movement  of 
the  sun  on   the    meridian,    with    the    consequent 
change  of  seasons,  and  the  stationary  appearance 
of  the  north  star. 

6.  In  addition  to  the  supposed  motion  of  the 
earth,  what  other  facts  must  be  associated  with  it  in 
order  to  fully  explain  what  has  been  mentioned  in 
the  previous  question? 


September]  ASTRONOMY.  49 

IV.  CONCERNING  THE  VARIATION  OF  LIGHT  AND 
HEAT  RECEIVED  FROM  THE  SUN  DURING 
THE  YEAB. 

Procure  a  scantling  about  fifteen  centimeters 
square,  one  meter  long,  and  square  the  ends. 
Fasten  one  end  of  this  by  means  of  a  hinge  to  a 
heavy  board,  about  thirty  centimeters  wide  and 
two  meters  long,  so  that  the  scantling  may  be  moved 
back  and  forth  from  a  perpendicular  to  a  horizontal 
position.  Fasten  the  board  solidly  to  the  ground, 
in  the  school  yard,  on  a  north  and  south  line  with 
the  free  end  of  the  scantling  to  the  south.  Attach 
to  one  side  of  the  scantling  a  small  brass  protractor 
with  its  straight  edge  either  at  right  angles  to  or 
parallel  with  the  upper  surface.  From  the  center 
of  the  arc,  suspend  a  shot  or  bullet  by  a  thread,  and 
it,  hanging  vertically,  will  indicate  the  degree  of 
slant  which  the  scantling  may  have.  As  soon  as 
practicable,  after  the  opening  of  the  school  year, 
on  a  day  when  the  sun  is  shining,  and  when  it  is 
on  the  meridian,  support  the  scantling  by  means 
of  a  block  underneath  so  that  it  will  cast  a  shadow 
from  its  cross  section  only.  It  is  evident  that  it 
will  then  have  the  same  slant  as  the  sun's  rays; 
and  if  we  regard  the  stick  of  wood  as  representing 
a  given  volume  or  beam  of  sunlight  and  heat,  it  is 
clear  that  the  area  of  the  shadow  cast  by  the  cross 
section  is  equal  to  the  area  covered  by  this  volume 
of  sunlight  and  heat.  Read  the  angle  of  elevation 
of  the  sun  at  this  time,  and  mark  and  measure  the 
area  of  the  shadow  cast  on  the  board.  From  week 
to  week,  by  moving  the  supporting  block  back, 


50  NUMBER  WORK.  [September 

the  scantling  can  be  readjusted  to  the  changing 
slant,  and  the  different  areas  covered  by  the  same 
volume  of  light  and  heat,  as  the  season  advances, 
may  be  measured  and  compared.  By  this  means 
it  will  be  shown  that  as  the  sun  moves  down  the 
meridian,  and  as  the  days  become  shorter,  a  given 
volume  of  light  and  heat  is  distributed  over  a 
larger  space,  and  consequently  its  effects  will  be 
less  upon  any  portion  of  that  area.  The  apparatus, 
here  described,  will  not  only  show  this  fact,  but 
it  will  furnish  a  means  for  comparatively  accurate 
measurement  in  which  the  area  of  the  cross  section 
of  the  stick,  representing  the  area  covered  by  this 
volume  of  rays  when  vertical,  may  be  used  as  a 
convenient  standard. 

PROBLEMS. 
I.     WHOLE  NUMBERS. 

1:  What  was  the  decrease  in  the  day's  length 
during  the  first  week?  During  the  second?  Dur- 
ing the  third?  During  the  fourth?  " 

2.  What    was    the    total  decrease  in   the  day's 
length  during  the  month  ? 

3.  How  many  minutes  did  the  day  lose  during 
each  week  at  evening  ?    During  the  entire  month  ? 

4.  How  many  minutes  did  the  day  lose  during 
each   week  in  the   morning?     During  the   entire 
month  ? 

5.  During  which   week  did  the  day  lose  most, 
and  how  much?    During  which  the  least,  and  how 
much  ? 

6.  What  is  the  difference  between  the  loss  in  the 
first  week  and  the  loss  in  the  last  week  of  the  month  ? 


September]  ASTRONOMY.  51 

7.  What  is  the  difference   between  the   length 
of    the   day  and  the  length  of  the   night  at   the 
beginning   of   the    month?     At    the    end   of    the 
month  ? 

8.  How  many  degrees  did  the  sun  move  down 
the  meridian  during  the  first  week?     During  the 
second?     During  the  third?     During  the  fourth? 

9.  How  many  degrees  did  the  sun  move  on  the 
meridian  during  the  month? 

10.  What  is  the  area  of  the  shadow  cast  at  the 
beginning  of  the  first  week  by  the  shadow-stick 
described  on  a  previous  page? 

11.  What  difference  in  area  between  the  shadow 
measured  first  and  that  cast  a  week  later?     Two 
weeks  later?     Three  weeks  later? 

II.     FRACTIONS. 

1.  What  part  of  the  day's  length  was  lost  during 
the  first  week?     During  the  second?     During  the 
third  ?     During  the  fourth  ? 

2.  What  part  of  the  day's  length  was  lost  during 
the  month? 

3.  What  part  of  the  loss  during  the  first  week 
was  in  the  morning?     During  the  second  week? 
During  the  third  week?   During  the  fourth  week? 

4.  What   part  of    the    entire    loss    during   the 
month  was  in  the  morning?     What  part  was  in 
the  evening? 

5.  What  part  of  the  loss  in  the  evening  equals 
the  loss  in  the  morning? 

0.  The  number  of  degrees  the  sun  has  moved 
on  the  meridian  during  the  month  equals  what 
part  of  the  distance  from  the  horizon  to  the  zenith  ? 


52  NUMBER  WORK.  [September 

7.  What  part  of  the  distance  traversed  on  the 
meridian  during  the  month  did  the  sun  move  dur- 
ing the  first  week?     During  the  second?     During 
the  third  ?     During  the  fourth  ? 

8.  The  distance  the  sun  is  above  the  southern 
horizon    at    noon,   when    the   day   and   night    are 
equal,    is    what    part    of    the    distance    from    the 
horizon  to  the  zenith  ? 

9.  The  area  of  the  cross  section  of  the  shadow- 
stick,  described  on  a  previous  page,  is  what  part 
of  the  area  of   the  shadow  cast  the   first  of   the 
month  ? 

10.  The  area  of  the  shadow  cast  at  the  begin- 
ning of  the  first  week  is  what  part  of  the  area  cast 
at  the  beginning  of  the  second?    The  third?    The 
fourth  ? 

III.     KATIO. 

1.  What  is  the  ratio  of  the  loss  of  the  day's 
length  during  the  first  week  to  the  loss  during  the 
second?     To  the  loss  during  the  third?     To  the 
loss  during  the  fourth? 

2.  What  is  the  ratio  of  the  loss  occurring  in  the 
morning  during  each  week  to  the  total  loss  in  the 
day's  length  for  the  same  time? 

3.  What    is   the    ratio   of   the   loss   during   the 
evening  of  each  week  to  the  total  loss  in  the  day's 
length  for  the  same  time? 

4.  What  is  the  ratio  of  the  loss  of  day's  length 
in  the  morning  during  each  week  to  the  loss  at 
evening  for  the  same  time  ? 

5.  What  is  the  ratio  of  the  average  of  the  day's 
length  during  the  first  week  to  the  average  length 


September]  ASTRONOMY.  53 

of  the  night?     During  the  second  week?     During 
the  third  week? 

6.  What  is  the  ratio  of  the  average  of  the  day's 
length  during  the  month  to  the  average  length  of 
night  ? 

7.  What  is  the  ratio  of  the  average  length  of 
day  during  the  first  week  to  the  average  length 
during  the  second  week?     To  the  average  length 
of  day  in  the  third  week?     To  the  average  length 
in  the  fourth  week  ? 

8.  What  is  the  ratio  of  the  length  of  night  at 
the  beginning  of  the  month  to  the  length  of  night 
at  the  end  of  the  month  ? 

9.  What  is  the  ratio  of  the  day's  length  at  the 
beginning,  to  its  length  at  the  end  of   the  month  ? 

10.  What  is  the  ratio  of  the  day's  length  at  the 
beginning  of  the  month  to  the  length  of  the  night 
at  the  same  time? 

11.  What  is  the  ratio  of  the   length  of  the  day 
at  the  end  of  the  month  to  the  length  of  the  night 
at  the  same  time? 

12.  What  is  the   ratio  of  the  area  of  the  cross 
section  of  the  shadow-stick,  described  on  a  previous 
page,  to  the  area  of  the  shadow   it  cast  at  the 
beginning  of  the  first  week? 

13.  What  is  the  ratio  of  the  area  of  the  shadow 
measured  the  first  week  to  that  measured  the  sec- 
ond ?     The  third  ?     The  fourth  ? 

IV.  PERCENTAGE. 

1.  What  per  cent  of    the  day's  length  is  lost 
during  the  first  week  of  the   month?     What  per 


54  NUMB&R  WORK.  [September 

cent  during  the  second  week?     During  the  third 
week  ?     During  the  fourth  week  ? 

2.  What  per  cent    of  the  day's  length  is  lost 
during  the   first  week  in   the   morning?     During 
the  second  week  ?  During  the  third  week  ?  During 

•  the  fourth  week? 

3.  What  per  cent  of  the  loss  of  the  day's  length 
during  the  month  occurs  in  the  morning? 

4.  What  per  cent  of  the  loss  of  the  day's  length 
for  the  month  occurs  in  the  evening? 

5.  What  per  cent  of  the  day's  length  is  lost 
during  the  month? 

6.  The  length   of   the  night   at   the  end  of  the 
month  is  what  per  cent  of  its  length  at  the  begin- 
ning? 

7.  The  length   of   the  day  at  the  end  of  the 
month  is  what  per  cent  of  its  length  at  the  begin- 
ning? 

8.  At  the  beginning  of  the  month,  the  length 
of  the  day  is  what   per  cent  of  the  length  of  the 
night? 

9.  The  length  of  the  day  is  what  per  cent  of  the 
length  of  the  night  at  the  end  of  the  month  ? 

10.  The  area  of  the  cross  section  of  the. shadow- 
stick,   described  on   a  previous  page,  is  what  pet- 
cent  of  the  area  of  the  shadow  measured  the  first 
week? 

11.  The  area  of  the  shadow  measured  the  first 
week    is    what    per   cent    of   that    measured    the 
second  ?     The  third  ?     The  fourth  ? 


GEOGRAPHY. 


NORTH    AMERICA-COAST    LINES    AND 
RELIEF. 

In  order  to  obtain  the  data  required  for  the  solution 
of  the  problems  given  in  geography,  it  will  be  neces- 
sary to  have  access  to  reliable  sources  of  geographical 
information.  By  sending  to  the  nearest  Weather 
Bureau  Station,  the  teacher  may  procure,  gratis, 
various  maps  and  monthly  summaries  which  will  be 
of  the  greatest  service.  With  these  and  a  good 
physical  geography,  such  as  Guyot's,  containing  maps 
and  tables  of  areas,-  hights,  lengths  of  rivers,  coast 
line,  etc.,  all  the  work  may  be  done.  The  problems 
have  been  given  with  a  view  to  assisting  the  pupil  to 
form  definite  and  clear  concepts  of  the  physical 
features,  with  their  relations  to  each  other,  and  of 
the  phenomena  of  climate  which  underlie  and,  to  so 
large  an  extent,  control  the  political,  commercial,  and 
social  life  of  the  people.  Lack  of  imagination  is  the 
great  obstacle  which  stands  in  the  way  of  pupils  in 
the  study  of  geography.  It  is  not  enough  that  one 
knows  that  the  Mississippi  River,  for  example,  flows 
through  a  valley,  but  he  must  know  something 
definite  about  the  extent  of  the  valley,  and  its  rela- 
tions to  other  similar  areas  adjacent  to  it.  Stimulated 
by  his  observations  on  the  country  about  him,  the 

55 


56  NUMBER  WORK.  [September 

pupil  must  be  taught  to  use  his  imagination  in  a 
rational  manner  concerning  those  parts  of  the  country 
which  lie  beyond  the  range  of  his  observation. 

PROBLEMS. 
I.     WHOLE  NUMBERS. 

A.  Coast  Lines. 

1.  Which    is    the    longer,  and  how   much,  the 
Atlantic  or  the  Pacific  coast  ? 

2.  Which    is  the   longer,  and    how  much,   the 
Atlantic  or  the  Arctic  coast? 

3.  Which    is  the   longer,  and   how  much,  the 
Atlantic  or  the  Gulf  coast? 

4.  Which    is  the   longer,  and    how   much,   the 
Arctic  or  the  Gulf  coast? 

5.  Which  is    the   longer,  and    how   much,   the 
Arctic  or  the  Pacific  coast? 

6.  Which   is  the    longer,   and    how   much,  the 
Gulf  or  the  Pacific  coast? 

7.  What   is  the    total  length   of   coast   line   of 
North  America? 

8.  For  every  hundred  square  miles  of   area  how 
much  coast  line  has  North  America  ? 

B.  Relief. 

Guyot  gives  the  following  classification  of  relief 
forms: 

ELEVATIONS  IN  MASS. — Plains  or  lowlands:     altitude  less 

than  one  thousand  feet. 
Alluvial:  formed  by  river  overflow. 
Marine:  sandy,  formed  under  sea  water. 
Undulating;    intermediate  between  marine  and  alluvial; 

rolling. 
Plateaus  or  table-lands:  altitude  over  one  thousand  feet. 


September]  GEOGRAPHY.  57 

Plateaus  of  the  first  order:    altitude  over  eight  thousand 
feet. 

Plateaus  of  the  second  order:  altitude  from  four  thousand 
to  eight  thousand  feet. 

Plateaus  of  the  third  order:  altitude  from  one  thousand  to 

four  thousand  feet. 

LINEAR  ELEVATIONS. — Mountains:   altitude  over  two  thou- 
sand feet.  Hills:  altitude  less  than  two  thousand  feet. 

9.  Which  is  greater,  and  how  much,  the  area  of 
table-lands  or  the  area  of  plains  in  North  America  ? 

10.  Which  is  greater,  and  how  much,  the  area 
of   the  plateaus  of  the  third  order  or  the  area  of 
those  of  the  second?     The  third  or  the  first? 

11.  Which  is  greater,  and  how  much,  the  area 
of  alluvial  plains  or  the  area  of  marine  plains? 

12.  Which  is  greater,  and  how  much,  the  area 
of  alluvial  plains  or  the  area  of  undulating  plains? 

13.  Which  is  greater,  and  how   much,  the  area 
of  the  marine  or  the  area  of  the  undulating  plains? 

14.  Which  is  greater,  and   how  much,  the  area 
of  the  plains  or  the  area  of  the  plateaus  of  the 
third  order? 

15.  Which  has  the  greater  plain  area,  and  how 
much,  the  northern  half  of  the  continent   or  the 
southern?     The  eastern  or  the  western? 

16.  Which  has  the  greater  plateau  area,  and  how 
much,  the  northern  half  or  the  southern?     The 
eastern  or  western  ? 

17.  Which  is  greater,  and  how  much,  the  area 
of  the  Pacific  highland  or  that  of   the  Atlantic 
highland? 

18.  Which  is  greater  in  length,  and  how  much, 
the  length  of  the  Rocky  Mountain  system  or  that 
of  the  Appalachian  ? 


58  NUMBER  WORK.  [September 

19.  Which  is  greater,  and  how  much,  the  average 
elevation  of  the  Rocky  Mountains  or  that  of  the 
Appalachian  ? 

20.  How  much  higher  than  the  average  eleva- 
tion of   the   system   is   the    highest    peak  in  the 
Rocky  Mountains? 

21.  How  much  higher  than  the  average  eleva- 
tion of   the  system  is  the    highest    peak   in  the 
Appalachian  Mountains  ? 

22.  How    much    difference    in    hight    is   there 
between  the  loftiest  peak  in  the  Rocky  Mountains 
and  the  loftiest  peak  in  the  Appalachian  system? 

II.     FRACTIONS. 
A.     Coast  Line. 

1.  The  length  of  the  Atlantic  coast  is  what  part 
of  the  length  of  the  Pacific  coast  ? 

2.  The  length  of  the  Gulf  coast  is  what  part  of 
the  length  of  the  Atlantic  coast  ? 

3.  The  length  of  the  Atlantic  coast  is  what  part 
of  the  length  of  the  Arctic  coast? 

4.  The  length  of  the  Gulf  coast  is  what  part  of 
the  length  of  the  Arctic  coast? 

5.  The  length  of  the  Gulf  coast  is  what  part  of 
the  length  of  the  Pacific  coast? 

6.  The  length  of  the  Arctic  coast  is  what  part 
of  the  length  of  the  Pacific  coast  ? 

7.  The  length  of  the  Atlantic  coast  is  what  part 
of  the  length  of  the  coast  line  of  the  entire  conti- 
nent? 

8.  The  length  of  the   Arctic  coast  line  is  what 
part  of  the  length  of    the   coast   line  of  the  entire 
continent  ? 


September]  GEOGRAPHY.  59 

9.  The  length  of  the  Gulf  coast  is  what  part  of 
the  length  of    the   coast    line   of  the  entire  conti- 
nent? 

10.  The  length  of  the  Pacific  coast  is  what  part 
of  the  length  of  the  coast  line  of  the  entire  conti- 
nent? 

11.  .bor  every  square  mile  of  area,  what  part  of 
a  mile  of  coast  line  in  North  America? 

B.     Relief. 

12.  The  area  of  the  plains  is  what  part  of  the 
area  of  the  plateaus  ? 

13.  The  area  of  the  alluvial  plains  is  what  part  of 
the  total-  plain  area  ? 

14.  What  part  of  the  plain  area  is  the  area  of 
the  marine  plains? 

15.  What  part  of  the  entire  plain  area  is  the 
area  of  the  undulating  plains  ? 

16.  The  area  of  the  alluvial  plains'  is  what  part 
of  the  area  of  the  marine  plains  ? 

17.  The  area  of  the  alluvial  plains  is  what  part 
of  the  area  of  the  undulating  plains  ? 

18.  The  area  of  the  marine  plains  is  what  part 
of  the  area  of  the  undulating  plains  ? 

19.  The  area  of  the  plains  is  what  part  of  the 
area  of  the  plateaus  of  the  third  order?     Of    the 
second?     Of  the  first?      . 

20.  The  area  of  the  plateaus  of  the  second  order 
is  what  part  of  the  area  of  those  of  the  first  order? 

21.  The  length  of  the  Appalachian  Mountain 
system  is  what  part  of  that  of  the  Rocky  Mountain 
system  ? 


60  NUMBER  WORK.  [September 

22.  The  average  hight  of  the  Rocky  Mountains 
is  what  part  of  the  hight  of  the  highest  peak  ? 

23.  The    average    hight    of    the    Appalachian 
Mountains  is  what  part  of  the  hight  of  the  highest 
peak? 

24.  The    average    hight    of     the    Appalachian 
Mountains  is  what  part  of  the  average  hight  of 
the  Rocky  Mountains? 

25.  The    hight   of    the    highest    peak    in    the 
Appalachian    Mountains    is    what    part    of    the 
hight  of   the  highest   peak  in  the  Rocky  Mount- 
ains? 

26.  The    highest    part   of    the    plateau    in    the 
western  highland    is    what    part    of    the    average 
hight  of  the  mountains? 

27.  The    highest    part    of    the    plateau   in   the 
eastern    highland   is    what    part    of    the    average 
hight  of  the  mountains? 

28.  The    average  hight    of  the    plateau  in  the 
eastern  highland  is  what  part  of  the  average  hight 
of  that  in  the  western  highland? 

III.     RATIO. 
A.     Coast  Lines. 

1.  The  length  of  the  Atlantic  coast  bears  what 
ratio  to  that  of  the  Pacific  coast? 

2.  The  length  of  the  Gulf  coast  bears  what  ratio 
to  that  of  the  Atlantic  coast  ? 

3.  The  length  of  the  Gulf  coast  bears  what  ratio 
to  that  of  the  Arctic  coast  ? 

4.  The  length  of  the  Atlantic  coast  bears  what 
ratio  to  that  of  the  Arctic  coast? 


September]  GEOGRAPHY.  61 

f).  Tin*  li'iiijtli  of  the  Gulf  coast  bears  what  ratio 

o 

to  that  of  the  Pacific  coast? 

(>.  The   length  of  the  Arctic  coast    bears    what 
ratio  to  that  of  the  Pacific  coast? 

7.  The  length  of  the  Atlantic  coast  bears  what 
ratio  to  that  of  the  entire  continent  ? 

8.  The  length  of  the  Pacific  coast  bears   what 
ratio  to  that  of  the  entire  continent  ? 

9.  The  length  of  the  Gulf  coast  bears  what  ratio 
to  that  of  the  entire  continent? 

10.  The  length  of  the  Arctic  coast  bears  what 
ratio  to  that  of  the  entire  continent? 

11.  The  number  of  square  miles  of  area  bears 
what   ratio  to   the  number  of  miles  of  coast  line  ? 

12.  What  is  the  ratio  of  the  actual  area  of  the 
continent  to  the  area  which  its  coast  line  might 
enclose  ? 

B.     Relief. 

13.  What  is  the  ratio  of  the  plain  area  to  the 
plateau  area? 

14.  What  is  the  ratio  of  the  alluvial  plain  area 
to  the  total  plain  area? 

15.  What  is  the  ratio  of  the  marine  plain  area 
to  the  total  plain  area? 

10.  What  is  the   ratio  of  the   undulating  plain 
area  to  the  total  plain  area? 

17.  What  is  the  ratio  of  the  alluvial  plain  area 
to  the  marine  plain  area? 

18.  What  is  the  ratio  of    the  alluvial  plain  area 
to    the  undulating  plain  area? 

19.  What  is  the  ratio  of  the  marine   plain  area 
to  the  undulating  plain  area  ? 


62  NUMBER  WORK.  [September 

20.  What  is  the  ratio  of  the  plain  area  to  that 
of  the  plateaus  of  the  third  order? 

21.  What  is  the  ratio  of  the  area  of  the  plateaus 
of  the  second  order  to  that  of  the  first  ? 

22.  What  is  the  ratio  of  the  area  of  the  plateaus 
of  the  third  order  to  the  entire  plateau  area  ? 

23.  What  is  the  ratio  of  the  area  of  the  plateaus 
of  the  second  order  to  the  entire  plateau  area? 

24.  What   is   the    ratio    of    the    length    of   the 
Appalachian  Mountain  system  to  that  of  the  Rocky 
Mountain  system? 

25.  What  is  the  ratio  of  the  average  hight  of 
the  Rocky  Mountain  system  to  that  of  the  highest 
peak? 

26.  What  is  the   ratio  of  the  average  hight  of 
the  Appalachian  Mountain  system  to  that  of  the 
highest  peak? 

27.  What  is  the  ratio  of  the  hight  of  the  highest 
peak  in  the  Appalachian  system    to   that  of  the 
highest  peak  in  the  Rocky  Mountain  system  ? 

28.  What  is   the   ratio  of  the  average  hight  of 
the  Appalachian  Mountain  system  to  the  average 
hight  of  the  Rocky  Mountain  system? 

29.  What  is  the  ratio  of  the  greatest   hight  of 
the  plateau  to  the  average  elevation  of  the  mount- 
ains in  the  western  highland? 

30.  What  is  the  ratio  of  the  greatest  hight  of 
the  plateau  in  the  eastern  highland  to  the  average 
elevation  of  the  mountain  chains? 

31.  The  greatest  hight  of  the  eastern   plateau 
bears  what  ratio  to  the  greatest  hight  of  the  west- 
ern? 


September]  GEOGRAPHY.  63 

32.  What   is  the   ratio  of  the  greatest  hight  of 
plateau  in  the  western   highland   to   the   hight  of 
the  highest  peak? 

33.  What  is  the  ratio  of  the  greatest  elevation 
of  the  plateau  in  the  eastern   highland  to  that  of 
the  highest  mountain  peak? 

IV.     PERCENTAGE. 
A.     Coast  Line. 

1.  The  length  of  the  Atlantic  coast  is  what  per 
cent  of  that  of  the  Pacific  coast? 

2.  The  length  of  the  Gulf  coast   is   what  per 
cent  of  that  of  the  Atlantic  coast? 

3.  The  length  of  the   Gulf  coast  is   what    per 
cent  of  that  of  the  Arctic  coast? 

4.  The  length  of  the  Arctic  coast  is  what  per 
cent  of  that  of  the  Atlantic  coast? 

5.  The  length  of   the  Gulf  coast  is  what  per 
cent  of  that  of  the  Pacific  coast? 

6.  The  length  of  the  Arctic  coast  is  what  per 
cent  of  that  of  the  Pacific  coast? 

7.  The  length  of  the  Atlantic  coast  is  what  per 
cent  of  that  of  the  entire  continent? 

8.  The  length  of  the  Pacific  coast  is  what  per 
cent  of  that  of  the  entire  continent? 

9.  The  length  of  the  Arctic  coast  is  what  per 
cent  of  that  of  the  entire  continent? 

• 

10.  The  length  of  the  Gulf  coast  is  what  per 
cent  of  that  of   the  entire  continent? 

11.  The  number  of  square  miles  of  actual  area 
in  North  America  is  what  per  cent  of  that  which 
could  be  enclosed  by  its  length  of  coast? 


64  NUMBER  WORK.  [September 

12.  The  number  of  square  miles  of  area  is  what 
per  cent  of  the  number  of  miles  of  coast  line  ? 
B.     Relief. 

13.  The  number  of  square  miles  in  the  plains 
equals  what  per  cent  of  the  number  in  the  plateaus  ? 

14.  The  number  of  square  miles  in  the  alluvial 
plains  equals  what  per  cent  of  the  number  in  the 
entire  plain  area? 

15.  The   number   of    square    miles   in    marine 
plains  equals  what  per  cent  of  the  number  in  the 
entire  plain  area? 

16.  The  number  of  square  miles  in  the  undulat- 
ing plain  area  equals  what  per  cent  of  the  entire 
plain  area? 

17.  The  number  of  square  miles  in  the  alluvial 
plain  area  equals  what  per  cent  of  the  number 
in  the  marine  plains? 

18.  The  number  of  square  miles  in  the  alluvial 
plain  area  equals  what  per  cent  of  the  number  in 
the  undulating  plains? 

19.  The  number  of  square  miles  in  the  marine 
plain  area  equals  what  per  cent  of  the  number  in 
the  undulating  plain? 

20.  The  number  of  square  miles  in  the  plain 
area  equals  what  per  cent  of  the  number  in  the 
plateaus  ? 

21.  The  number  of  square  miles  in  the  plateaus 
of   the  second  order  equals  what  per  cent  of  the 
number  in  the  third? 

22.  The  number  of  square  miles  in  the  plateaus 
of  the  third  order  equals  what  per  cent   of  the 
number  in  the  entire  plateau  area? 


September]  GEOGRAPHY.  05 

23.  The  number  of  square  miles  in  the  plateau 
area  equals  what  per  cent  of  the  number  in   the 
entire  continent? 

24.  The  number  of  square  miles  in  the  plains 
equals   what  per  cent  of  the  number  in  the  entire 
continent  ? 

•J~>.  The  length  of  the  Appalachian  Mountain 
system  equals  what  per  cent  of  the  length  of  the 
Rocky  Mountain  system  ? 

26.  The  average  elevation  of  the  Appalachian 
Mountains  equals  what   per  cent  of  that   of  the 
Rocky  Mountains? 

27.  The  average  elevation  of  the  Rocky  Mount- 
ains equals  what    per  cent  of   the   hight  of   the 
highest  peak? 

28.  The  average  elevation  of  the  Appalachian 
Mountains  equals   what  per  cent  of  the  hight  of 
the  highest  peak  ? 

29.  The  elevation  of  the  highest  peak  in  the 
Appalachian  Mountains  equals  what  per  cent  of  the 
hight  of  the  highest  peak  in  the  Rocky  Mountains  ? 

30.  The  greatest  plateau  elevation  in  the  west- 
ern highland  equals  what  per  cent  of  the  average 
elevation  of  the  mountains? 

31.  The  greatest  plateau  elevation  in  the  east- 
ern highland  equals  what  per  cent  of  the  average 
hight  of  the  mountains? 

82.  The  greatest  elevation  of  the  plateau  in  the 
western  highland  equals  what  per  cent  of  that  of 
the  highest  peak? 

33.  The  greatest  elevation  of  the  plateau  in  the 
eastern  highland  equals  what  per  cent  of  that  of 
the  highest  peak? 


MINERALOGY. 


THE    MECHANICAL   CONSTITUENTS  OF 
SOILS. 

The  following  lessons  are  intended  to  accompany 
geography  work  on  the  subject  of  erosion,  transporta- 
tion and  deposition  of  soils.  In  making  the  required 
analysis  two  small  sieves  about  eight  centimeters 
square  and  three  centimeters  deep  will  be  required; 
the  first  to  have  wire  gauze  with  one-tenth-inch  mesh 
and  the  second  with  gauze  one-fiftieth  of  an  inch 
mesh.  In  addition  to  these  a  tall  bottle  or  jar  will 
be  required.  To  gather  the  necessary  data,  proceed 
as  follows: 

1.  Select  a  sample  of  soil  of  average  composition 
and  dry  it. 

2.  Rub  up  the  lumps  and  pass  a  definite  amount 
— about  twenty   grams — through  the  coarse    sieve. 
Wash,  dry,   and   weigh  the  part  too  coarse  to  pass 
through  and  this  will  give  the  coarse  gravel. 

3.  Rub  the  part  which  passed  through  the  coarse 
sieve  through  the  fine  sieve.     Wash,  dry,  and  weigh 
the  part  too  coarse  to  pass  through  and  this  will  ^give 
the  gravelly  sand. 

4.  Weigh  a  definite  amount  of  the  gravelly  sand 
and  heat  it  red  hot  in  a  Battersea  dish ;  the  loss  will 
be  the  weight  of  organic  matter. 


September]  MINERALOGY.  67 

* 

5.  Weigh  a  definite  amount — about  fifteen  grams 
— of  the  gravelly  sand  and  separate  the  particles  by 
shaking  or  boiling  in  a  flask ;  rinse  it  out  into  a  tall 
jar  with  a  wide  mouth.     Set  the  jar  in  a  larger  ves- 
sel to  catch   the   overflow   and  then   by   means  of  a 
gentle  stream  of  water  and  agitation  wash  until  the 
water  runs  away  clear.    Dry  and  weigh  what  remains, 
and  this  will  be  the  coarse  sand.     Heat  a  definite 
amount  of  this  in  a  Battersea  dish  to  find  the  organic 
matter. 

6.  Repeat  the  process  described  in  (5)  with  the 
overflow  with  less  agitation  and  the  result  will  be  the 
fine  sand.     Heat  as  before  for  the  organic  matter. 

1.  Subtract  the  weight  of  the  coarse  and  fine  sand 
from  the  weight  taken  in  the  beginning  and  the  result 
will  be  the  clay  in  the  soil. 

The  several  steps  employed  in  mechanical  analysis 
are  here  given,  but  with  pupils  beginning  the  work 
not  so  much  should  be  attempted.  The  teacher  must 
determine  how  much  can  be  intelligently  done  by  the 
pupils. 

These   operations  will  furnish  the  following  data: 

1.  The  coarse  gravel. 

2.  The  gravelly  sand. 

3.  The  organic  matter. 

4.  The  coarse  sand. 

5.  The  fine  sand. 

6.  The  clay. 

PROBLEMS. 
I.     WHOLE  NUMBERS. — ( Use  from  twenty-five  to  fifty 

grams.} 

1.  Which   weighs    more,   and    how    much,    the 
coarse  gravel  or  the  gravelly  sand? 


68  NUMBER  WORK.  [September 

2.  Which    weighs   more,    and    how   much,    the 
coarse  gravel  or  the  organic  matter? 

3.  Which    weighs    more,    and   how    much,   the 
coarse  gravel  or  the  coarse  sand  ? 

4.  Which    weighs    more,  and    how    much,    the 
coarse  gravel  or  the  fine  sand? 

5.  Which   weighs   more,    and    how    much,    the 
coarse  gravel  or  the  clay? 

6.  Which    weighs    more,    and    how    much,  the 
gravelly  sand  or  the  organic  matter? 

7.  Which    weighs    more,    and  how   much,    the 
gravelly  sand  or  the  coarse  sand? 

8.  Which    weighs    more,    and    how    much,  the 
gravelly  sand  or  the  fine  sand? 

9.  Which    weighs    more,   and  how   much,  the 
gravelly  sand  or  the  clay  ? 

10.  Which  weighs   more,   and   how  much,   the 
organic  matter  or  the  coarse  sand? 

11.  Which  weighs   more,   and  how   much,   the 
organic  matter  or  the  fine  sand  ? 

12.  Which   weighs   more,   and  how  much,   the 
organic  matter  or  the  clay  ? 

13.  Which   weighs  more,  and  how  much,   the 
coarse  sand  or  the  fine  sand  ? 

14.  Which  weighs  more,   and  how  much,  the 
coarse  sand  or  the  clay  ? 

15.  Which   weighs   more,   and   liow   much,  the 
fine  sand  or  the  clay  ? 

II.     FRACTIONS. 

1.  What  part  of  the  weight  of  the  soil  is  the 
weight  of  the  coarse  sand  ? 


September]  MINERALOGY.  69 

2.  What    part    of    the    weight   of    the    soil    is 
the  weight  of  the  gravelly  sand? 

3.  What   part   of    the    weight   of    the    soil    is 
the  weight  of  the  organic  matter? 

4.  What  part  of  the  weight  of  the  soil  is  the 
weight  of  the  fine  sand? 

5.  What  part  of  the   weight  of  the  soil  is  the 
weight  of  the  clay  ? 

6.  The  weight  of  the  coarse  gravel  is  what  part 
of  the  weight  of  the  gravelly  sand  ? 

7.  The  weight  of   the  organic  matter  is   what 
part  of  the  weight  of  the  clay  ? 

8.  The   weight  of  the  organic  matter  is  what 
part  of  the  weight  of  the  fine  sand? 

9.  The  weight  of  the    organic    matter  is  what 
part  of  the  weight  of  the  coarse  sand? 

10.  The  weight  of  the  organic  matter'  is  what 
part  of  the  weight  of  the  clay?     Of  the  fine  sand? 
Of  the  coarse  sand? 

11.  The  weight  of  the  clay  is  what  part  of  the 
weight  of  the  fine  sand?     Of    the    coarse    sand? 
Of  the  organic  matter? 

12.  The  weight  of  the  fine  sand  is  what  part  of 
the  weight  of  the  coarse  sand? 

13.  The  weight  of  the  fine  sand  is  what  part  of 
the  weight  of  the  gravelly  sand? 

14.  The  weight  of  the  coarse  sand  is  what  part 
of  the    weight  of    the  gravelly    sand    and  coarse 
gravel  ? 

15.  The  weight  of   the  coarse   gravel  is   what 
part  of  the  weight  of  the  gravelly  sand?     Of  the 
coarse  sand?     Of  the  fine  sand? 


70  NUMBER  WORK.  [September 

III.     RATIO. — (By  weight.} 

1.  What  is  the  ratio  of  the  coarse  gravel  to  the 
soil? 

2.  What  is  the  ratio  of  the  gravelly  sand  to  the 
soil? 

3.  What   is  the   ratio  of  the  organic  matter  to 
the  soil? 

4.  What  is   the  ratio  of  the  coarse  sand  to  the 
soil? 

5.  What   is   the  ratio  of   the   fine   sand   to   the 
soil? 

6.  What  is  the  ratio  of  the  clay  to  the  soil? 

7.  What  is  the  ratio  of  the  coarse  gravel  to  the 
gravelly  sand? 

8.  What  is  the  ratio  of  the  coarse  gravel  to  the 
organic  matter? 

9.  What  is  the  ratio  of  the  coarse  gravel  to  the 
coarse  sand? 

10.  What  is  the  ratio  of  the  coarse  gravel  to 
the  fine  sand? 

11.  What   is   the   ratio  of  the   coarse   gravel  to 
the  clay? 

12.  What  is   the   ratio  of  the  gravelly  sand  to 
the  organic  matter? 

13.  What   is  the  ratio  of  the  gravelly  sand  to 
the  coarse  sand? 

14.  What  is  the  ratio  of    the  gravelly  sand  to 
the  fine  sand? 

15.  What  is  the  ratio  of   the   gravelly  sand  to 
the  clay? 

16.  What    is   the  ratio  of  the    organic    matter- 
to  the  coarse  sand? 


September]  MINERALOGY.  71 

17.  What  is   the   ratio  of   the  organic    matter 
to  the  fine  sand? 

18.  What  is    the   ratio  of    the  organic    matter 
to  the  clay? 

19.  What  is  the  ratio  of  the  coarse  sand  to  the 
fine  sand? 

20.  What  is  the  ratio  of  the  coarse  sand  to  the 
clay? 

21.  What  is  the  ratio  of  the  fine  sand  to  the 
clay? 

IV.     PERCENTAGE. — (By  weight.] 

1.  The  coarse  gravel  equals  what  per  cent  of  the 
soil? 

2.  The  gravelly  sand  equals  what  per  cent  of 
the  soil? 

3.  The  organic  matter  equals  what  per  cent  of 
the  soil? 

4.  The  coarse  sand  equals  what  per  cent  of  the 
soil? 

5.  The  fine  sand  equals  what  per  cent  of  the  soil  ? 

6.  The  clay  equals  what  per  cent  of  the  soil  ? 

7.  The  clay  equals    what  per  cent   of  the  fine 
sand? 

8.  The  clay  equals  what  per  cent  of  the  coarse 
sand? 

9.  The  clay  equals  what  per  cent  of  the  organic 
matter? 

10.  The  clay  equals  what  per  cent  of  the  fine 
sand?  Of  the  coarse  sand?    Of  the  gravelly  sand? 

11.  The  fine  sand  equals  what  per  cent  of  the 
coarse  sand  ?    Of  the  gravelly  sand  ?   Of  the  coarse 
gravel ? 


72  NUMBER  WORK.  [September 

12.  The  coaoe  sand  equals  what  per  cent  of  the 
gravelly  sand?    Of  the  coarse  gravel?    Of  the  fine 
sand? 

13.  The  organic  matter  equals  what  per  cent  of 
the  fine  sand  ?     Of  the  coarse  sand  ?    Of  the  clay  ? 

14.  The  gravelly  sand  equals  what  per  cent  of 
the  coarse  sand  and  fine  sand? 

15.  The  coarse  gravel  equals  what  per  cent  of 
the  gravelly  sand?     Of  the  coarse  sand?     Of  the 
fine  sand? 

16    The  coarse  gravel  and  gravelly  sand  equal 
what  per  cent  of  the  soil? 


ZOOLOGY. 


STUDY  OF  ANIMAL  TISSUES. 

It  is  usually  given  to  pupils,  as  a  matter  of  infor- 
mation, that  bone  and  other  animal  tissues  are  com- 
posed of  animal  and  mineral,  that  is,  of  organic  and 
inorganic  matter.  It  is  not  very  difficult  to  have 
pupils  perform  certain  experiments  which  will  show 
in  definite  results  the  approximate  amount  of  the 
different  constituents.  The  following  problems  have 
been  prepared  with  respect  to  bone  and  muscle,  but 
they  may  be  adapted  to  the  study  of  any  other  tissue. 
For  the  purpose  of  the  study,  secure  some  small 
pieces  of  well-bleached  bone  and  pound  or  grind 
them  up  rather  fine.  Weigh  a  small  amount  — 
about  five  grams — and  place  in  a  battersea  dish  over 
the  alcohol  or  bunsen  flame.  When  reduced  to  a 
fine  grayish  white  ash  .weigh  again  and  note  the  loss. 
This  will  give  the  following  data: 

1.  Weight  of  the  dried  or  bleached  bone. 

2.  Weight  of  organic  matter;  this   is  the  weight 
lost  by  burning. 

3.  Weight  of  ash  or  inorganic  matter. 

The  periosteum  and  adhering  fat  may  be  cleaned 
from  a  fresh  bone  and  a  small  piece,  after  being  dried, 
may  be  weighed.  By  soaking  this  in  dilute  hydro- 
chloric acid  the  mineral  matter  will  _be  removed. 

73 


74  NUMBER  WORK.  [October 

When  soft  and  flexible  the  part  remaining  should  be 
thoroughly  dried  and  weighed.  This  will  give  the 
amount  of  organic  matter  in  the  fresh  bone.  The 
difference  between  this  and  the  weight  of  the  fresh 
bone  will  give  the  weight  of  the  inorganic  matter 
which  was  removed  by  the  acid. 

PROBLEMS. 
I.     WHOLE  NUMBERS. 

1.  How  much  greater  is  the  weight  of  the  dry 
bone  than  the  weight  of  the  ash  it  contains? 

2.  How  much  greater  is  the  weight  of  the  dry 
bone  than  the  weight  of  the  organic    matter   it 
contains  ? 

3.  Which  is  greater,  and  how  much,  the  weight 
of  the  organic  matter  or  the  weight  of  the  ash  ? 

4.  The  weight  of  the  organic  matter  obtained 
by  soaking  the  bone  in  acid  is  how  much  less  than 
that  of  the  fresh  bone  ? 

5.  The  weight  of  the  mineral   matter  lost   by 
soaking  the  bone  in  acid  is  how  much   less  than 
the  weight  of  the  fresh  bone? 

6.  The  wreight   of   the   mineral  matter  lost  by 
soaking  the  bone  in  acid  is  how  much  less  than 
the  weight  of  the  organic  matter? 

7.  What  is  the  difference  between  a  given  weight 
of  a  piece  of  muscle  and  the  weight  of  the  ash  it 
contains  ? 

8.  What  is  the  difference  between  a  given  weight 
of  a  piece  of  muscle  and  the  weight  of  the  organic 
matter  in  it? 

9.  Which  is  greater  in  weight,  and  how  much. 


October]  ZOOLOGY.  75 

the  ash  in  a  bone  or  the  ash  in  a  piece   of  muscle 
of  equal  weight? 

10.  Which  is  greater  in  weight,  and  how  much, 
the  organic  matter  in  a  bone  or  the  organic  matter 
in  a  piece  of  muscle  of  equal  weight? 
II.     FRACTIONS. 

1.  The  weight  of  the  ash  equals  what  part  of 
the  weight  of   the  entire  bone  ? 

2.  The  weight  of  the   ash   equals  what  part  of 
the  weight  of  the  organic  matter? 

3.  The    weight   of   the   organic    matter  equals 
what  part  of  the  weight  of  the  entire  bone? 

4.  The    weight   of   the    organic    matter   equals 
what  part  of  the  weight  of   the  ash? 

5.  The  weight  of  the  entire  bone  equals  what 
part  of   the  weight  of  the  ash? 

6.  The  weight  of  the  entire  bone  equals  what 
part  of  the  weight  of  the  organic  matter? 

7.  The  weight  of  a  human  skeleton  is  twenty  - 
four  pounds;  what  part  of   the  weight  of   an  aver- 
age man  is  it? 

8.  What  is  the  weight  of  ash  in  a  human  skel- 
eton of  twenty-four  pounds'  weight? 

9.  What  is  the  weight  of  organic  matter  in  a 
human  skeleton  of  twenty-four  pounds'  weight? 

10.  The  weight  of  ash  in  the  skeleton  is  what 
part  of  the  weight  of   an  average  man? 

11.  The  weight  of  organic  matter  in  a  skeleton 
is  what   part  of   the  entire  weight  of  an  average 
man  ? 

12.  What   part  of  the   weight  of  muscle  is  the 
weight  of  the  ash  which  it  contains. 


76  NUMBER  WORK.  [October 

13.  What   part  of  the  weight  of   muscle  is  the 
organic  matter  which  it  contains? 

14.  The  weight  of  the  ash  equals  what  part  of  the 
weight  of  the  organic  matter  in  a  piece  of  muscle  ? 

15.  The  ash  found  in  a  given  weight  of  muscle 
equals  what  part  of  that  found  in  the  same  weight 
of  bone? 

16.  The  organic  matter  found  in  a  given  weight 
of  muscle  equals   what  part  of  that   found  in  the 
same  weight  of  bone  ? 

17.  The  muscle  forms  forty-two  hundredths  of 
a  man's  weight;   how  much  ash  does  it  contain? 

18.  How  much  organic  matter  in  the  muscles  of 
an  average-sized  man  ? 

III.     RATIO. 

1.  What  is   the  ratio,  by  weight,  of  the  ash  to 
the  entire  bone  ? 

2.  What  is  the  ratio,  by  weight,  of  the  ash  to 
the  organic  matter? 

3.  What  is  the  ratio,  by  weight,  of  the  organic 
matter  to  the  entire  bone? 

4.  What  is  the  ratio,  by  weight,  of  the  organic 
matter  to  the  ash  ? 

5.  What  is  the  ratio,  by   weight,  of  the  entire 
bone  to  the  organic  matter  it  contains? 

6.  What  is  the  ratio,  by  weight,  of  the   entire 
bone  to  the  ash  it  contains? 

7.  The  weight  of  a  human  skeleton  is  twenty- 
four  pounds ;  what  weight  of   ash  does  it  contain  ? 
What  weight  of  organic  matter? 

8.  What  is  the  ratio,  by   weight,  of  the  ash  in 
the  skeleton  to  the  average  weight  of  a  man? 


October]  ZO&LOGY.  77 

(.».  What  is  the  ratio,  by  weight,  of  the  organic 
matter  in  the  skeleton  to  the  average  weight  of 
a  man  ? 

10.  What  is  the  ratio,  by  weight,  of  the  skeleton 
to  the  average  weight  of  a  man? 

11.  What  is  the  ratio,  by  weight,  of  the  ash  in 
muscle  to  the  entire  weight  of  the  muscle? 

12.  What  is  the  ratio,  by  weight,  of  the  organic 
matter  in   muscle    to    the    entire    weight  of   the 
muscle  ? 

13.  What  is  the   ratio,  by  weight,  of  the  ash  in 
muscle  to  the  organic  matter  which  it  contains? 

14.  What  is  the  ratio,  by   weight,  of  the  ash 
found  in  muscle  to  the  ash  found  in  bone? 

15.  What  is  the  ratio,  by  weight,  of  the  organic 
matter  found  in  muscle  to  the  organic  matter  found 
in  bone? 

16.  The  muscles  form  forty -two  hundredths  of 
the    entire    weight   of  man;  how    much    ash,    by 
weight,  does  this  amount  of  muscle  contain? 

17.  How  much  organic  matter,  by  weight,  in  the 
muscles  of  an  average  man? 

IV.     PERCENTAGE. 

1.  What  per  cent,  by  weight,  is  the  ash  of  the 
entire  bone? 

2.  What  per  cent,  by  weight,  is  the  ash  of  the 
organic  matter  in  bone? 

3.  What   per  cent,   by  weight,   is  the   organic 
matter  of  the  entire  bone? 

4.  What  per  cent  of  the  weight  of  the  organic 
matter  equals  the  weight  of  the  ash  ? 


78  NUMBER  WORK.  [October 

5.  The  weight  of  a  human  skeleton  is  twenty- 
four  pounds;  how  much  ash,  by  weight,  does  it 
contain  ?     How  much  organic  matter  ? 

6.  What  per  cent  of  an  average  man's  weight  is 
his  skeleton? 

7.  What  per  cent  of  an  average  man's  weight  is 
the  ash  in  his  skeleton  ? 

8.  What  per  cent  of  an  average  man's  weight 
is  the  organic  matter  in  the  skeleton  ? 

9.  What  per  cent  of  a  given  weight  of  muscle 
equals  the  weight  of  the  ash? 

10.  What  per  cent  of  a  given  weight  of  muscle 
equals  the  weight  of  the  organic  matter? 

11.  The  ash  in  muscle  equals  what  per  cent,  by 
weight,  of  the  organic  matter? 

12.  The  ash  found  in  a  given  weight  of  muscle 
equals  what  per  cent  of  that   found  in  the  same 
weight  of  bone? 

13.  The  organic  matter  found  in  muscle  equals 
what  per  cent,  by  weight,   of  that  found  in    the 
same  weight  of  bone  ? 

14.  The  muscles  form  forty -two  hundredths  of 
a  man's  weight;    how   much   ash   in   an    average 
man's  muscle? 

15.  How  much   organic   matter  in  an  average 
man's  muscle? 


BOTANY. 


ANNUAL    GROWTH    OF    BRANCHES    OF 
TREES. 

The  motive  for  the  following  lessons  is  to  lead  the 
pupil  to  investigate  the  laws  of  growth  which  prevail 
in  different  trees  by  which  their  forms  are  deter- 
mined. Each  kind  of  tree,  when  uninfluenced  by 
accidental  surroundings,  seems  to  grow  according  to 
a  certain  type  form  from  which  individuals  vary  but 
little.  Why  a  certain  typical  form  should  be  found 
to  include  the  greater  number  of  the  individuals  of  a 
particular  kind  of  tree  is  a  question  not  easily 
answered.  Knowing,  however,  the  functions  of  the 
leaf  in  its  two-fold  capacity  as  lungs  and  stomach, 
and,  for  the  proper  performance  of  these  functions, 
its  dependence  upon  sunlight  and  air,  it  is  fair  to 
conclude  that  the  growth  and  distribution  of  branches 
is  such  as  will  insure  the  greatest  exposure  of  leaf 
surface  to  these  influences.  Many  other  factors 
enter  into  the  problem,  such  as  the  angle  the  branches 
make  with  the  main  stem,  the  shape  and  arrange- 
ment of  the  leaves,  the  relation  of  the  terminal  to  the 
lateral  growth,  and  the  relation  of  the  dormant  to 
the  active  buds.  Some  of  these  will  be  considered 
in  another  place.  When  the  type  form  of  a  tree  is 
discovered,  the  general  symmetry  of  the  tree  within 

79 


80  NUMBER  WORK.  [October 

the  general  form  is  the  most  striking  feature ;  yet  closer 
observation  will  reveal  more  or  less  asymmetry,  so 
that  the  different  sides  of  the  tree  may  be  considered 
as  measures,  relatively,  of  the  different  influences  or 
forces  which  play  upon  them  and  upon  the  tree  as  a 
whole.  The  results  should  thus  indicate  something 
of  the  mutual  relations  of  the  tree  and  its  environ- 
ment. 

It  is  intended  that  the  following  observations  and 
measurements  should  be  made: 

1.  As  large  a  number  of  measurements  as  practi- 
cable of  the  terminal  growths  on  each  side  of  the  tree. 

2.  Similar   measurements    of    the    growths    from 
lateral  buds. 

3.  The  length  of  the  terminal  and  lateral  growths  of 
one  or  more  of  the  preceding  years,  taken  from  each 
side  of  the  tree. 

4.  The    measurement   of    the  greatest  spread  of 
branches;  hold  a  plumb  line  under  the  end  of  the 
longest  branch  and  measure  on  the  ground  the  dis- 
tance from  the  line  to  the  trunk. 

PROBLEMS. 
I-     WHOLE  NUMBERS. 
A.     The  present  year. 

1.  What  is  the  average  length  of  the  growths 
from  the  terminal  buds  on  the  north  side  of  the 
tree? 

2.  What  is  the  average  length  of  the  growths 
f  ronj  the  lateral  buds  on  the  north  side  of  the  tree  ? 

3.  What  is  the  average  length  of  the  growths 
from  the  terminal  buds  on   the  south  side  of  the 
tree? 


October]  BOTA^Y  81 

4.  What  is  the  average  length  of  the  growths 
from  the  lateral  buds  on  the  south  side  of  the  tree? 

5.  What  is  the  average  length  of  the  growths 
from  the  terminal  buds  on  the  east  side  of  the  tree  ? 

G.  What  is  the  average  length  of  the  growths 
from  the  lateral  buds  on  the  east  side  of  the  tree? 

7.  What  is  the  average  length  of  the  growths 
from  the  terminal  buds  on  the  west  side  of  the  tree  ? 

8.  What  is  the  average  length  of  the  growths 
from  the  lateral  buds  on  the  west  side  of  the  tree? 

9.  Which    side    of   the    tree   had   the   greatest 
average  terminal  growth,  and  how  much? 

10.  Which  side  of   the  tree  had   the  greatest 
average  lateral  growth,  and  how  much? 

11.  Which   is  the  greater,  and  how   much,  the 
average  terminal   growth    or  the  average   lateral 
growth  on  each  side  of  the  tree? 

12.  Which  is  the  greater,  and  how  much,  the 
average    terminal  growth  or  the    average    lateral 
growth  on  the  entire  tree? 

13.  What  is  the  horizontal  distance   from  the 
trunk  through  which   the  longest  branch   extends 
on  the  north  side  of  the  tree? 

14.  What  is  the  horizontal   distance    from  the 
trunk  through  which  the  longest  branch  extends 
on  the  south  side  of  the  tree? 

15.  What  is  the  horizontal  distance    from  the 
trunk  through  which  the  longest  branch  extends 
on  the  east  side  of  the  tree  ? 

16.  What  is  the  horizontal  distance    from  the 
trunk  through  which   the   longest  branch  extends 
on  the  west  side  of  the  tree? 

&n&Stif^ 


CHIVEB8ITY 


82  NUMBER  WORK.  [October 

17.  What  is  the  difference  between  the  length 
of    the   longest   branch   on  the  north  side  of  the 
tree  and  the  length  of  the  longest  -branch  on  the 
south  side?     Compare  those  on  the  east  and  west 
sides. 

B.     The  preceding  year. — (Note  whether  or  not  the 
•    tree  has  reached  its  maturity.) 

18.  Which  is  greater,  and  how  much,  the  average 
terminal  growth  or  the  average  lateral  growth  on 
the  north  side? 

19.  Which  is  greater,  and  how  much,  the  aver- 
age terminal  growth  or  the  average  lateral  growth 
on  the  south  side? 

20.  Which  is  greater,  and  how  much,  the  aver- 
age terminal  growth  or  the  average  lateral  growth 
on  the  east  side? 

21.  Which  is  greater,  and  how  much,  the  aver- 
age terminal  growth  or  the  average  lateral  growth 
on  the  west  side? 

22.  In    which    year   was    the    terminal   growth 
greater  on  each  side ;  how  much  greater  was  it  ? 

23.  In  which  year  was  the  lateral  growth  greater 
on  each  side ;  how  much  greater  was  it  ? 

24.  Which   of   the  following  has   the   greatest 
average    terminal  growths,    and    how    much,    the 
maple,  the  willow,  the  oak,  the  ash,  the  box-elder, 
the  elm  ? 

25.  Which  of   the    following   has   the  greatest 
average  lateral  growths,  and  how  much,  the  maple, 
the   willow,  the  oak,  the  ash,  the  box-elder,   the 
elm  ? 


October]  BOTANY.  83 

II.     FRACTIONS. 

A.     The  present  year. 

1.  The  average  growth  of  the  twigs  on  the  north 
side  of  the  tree  from  the  lateral  buds  equals  what 
part  of    the    average   growth  from    the    terminal 
buds? 

2.  The  average  growth  of  the  twigs  on  the  south 
side  of  the  tree  from  the  lateral  buds  equals  what 
part   of    the   average  growth    from    the    terminal 
buds? 

3.  The  average  growth  of  the  twigs  on  the  east 
side  of  the  tree  from  the  lateral  buds  equals  what 
part  of  the    average    growth    from    the    terminal 
buds? 

4.  The  average  growth  of  the  twigs  on  the  west 
side  of  the  tree  from  the  lateral  buds  equals  what 
part  of   the  average    growth    from    the    terminal 
buds? 

5.  The   average  terminal  growth  on  the  north 
side  equals  what  part    of    the  average    terminal 
growth  on  the  south  side? 

0.  The  average  lateral  growth  on  the  north  side 
equals  what  part  of  the  average  lateral  growth  on 
the  south  side? 

7.  The  average  terminal  growth  on  the  east  side 
equals  what  part  of   the  average   terminal  growth 
on  the  west  side? 

8.  The  average  lateral  growth  on  the  east  side 
equals  what  part  of  the  average  lateral  growth  on 
the  west  side? 

9.  The  average  lateral  growth  of  the  twigs  on 


84    ,  NUMBER  WORK.  [October 

the   entire  tree  equals  what  part  of  the   average 
terminal  growth  of  the  twigs? 

10.  The  horizontal  distance  through  which  the 
longest  branch  on  the  north  side  of  the  tree  extends 
from  the  trunk  equals  what  part  of  the  distance 
through  which   the  longest  branch  extends  on  the 
south  side? 

11.  The  horizontal  distance  through  which  the 
longest  branch  on  the  east  side  of  the  tree  extends 
from  the  trunk  equals  what  part  of  the  distance 
through  which  the  longest  branch  extends  on  the 
west  side? 

12.  The  horizontal  distance  through  which  the 
longest  branch  extends  on  the  north  side  of   the 
tree   equals    what    part  of   the   distance   through 
which   the    longest    branch    extends    on   the   east 
side  ?     Compare  the  west  side. 

13.  The  horizontal  distance  through  which  the 
longest  branch  extends  on  the  south  side  of  the 
tree  equals   what    part  of   the    distance   through 
which    the    longest   branch    extends    on    the   east 
side  ?     Compare  the  west  side. 

14.  The  average  terminal  growth  on  the  north 
side  of  the  tree  equals  what  part  of  the  average 
terminal  growth  on  the  east  side?     On  the  west 
side? 

15.  The  average   lateral   growth  on    the  north 
side  of  the  tree  equals  what  part  of  the  average 
lateral    growth   on   the   east  side?     On   the   west 
side? 

16.  The  average  terminal  growth  on  the  south 
side  of  the  tree  equals  what  part  of  the  average 


October]  BOTANY.  85 

terminal  growth  on  the  east  side?     On  the  west 
side? 

17.  The  average  lateral    growth   on  the  south 
side  of  the  tree  equals  what   part  of  the  average 
lateral  growth  on  the  east  side  ?  On  the  west  side  ? 
B.     The  preceding  year. — (Note  whether  or  not  the 

tree  has  reached  its  maturity.) 

18.  The  average  terminal  growth  on  each  side 
of  the  tree  equals  what  part  of  the  average  ter- 
minal growth  for  the  present  year? 

19.  The  average  lateral  growth  on  each  side  of 
the  tree  equals, what  part  of  the  average  lateral 
growth  for  the  present  year? 

20.  The  average  terminal  growth  for  the  entire 
tree    equals    what    part  of    the    average   terminal 
growth  for  the  present  year? 

21.  The   average  lateral  growth  for  the  entire 
tree    equals    what    part   of    the    average    lateral 
growth  for  the  present  year? 

22.  The   average   terminal  growth  of   the    oak 
equals  what  part  of  the  average  terminal  growth 
of  the  maple?     Of  the  ash?     Of  the  willow?     Of 
the  box-elder?     Of  the  elm? 

23.  The  average  lateral  growth  of  the  oak  equals 
what  part   of  the   average   lateral    growth  of  the 
maple?     Of   the   ash?     Of  the   willow?     Of    the 
box-elder?     Of  the  elm? 

24.  The  length  of  the  greatest  horizontal  diam- 
eter of  the  top  of  the  oak  equals  what  part  of  the 
length  of  the  vertical  diameter  of  the  top? 

25.  Compare  as  in    (24)    the  two  diameters  of 
the  ash,  the  maple,  the  box-elder,  and  the  elm? 


86  NUMBER  WORK.  [October 

III.     KATIO. 

A .     The  present  year. 

1.  The  average  growth  of  the  lateral  twigs  on 
the  north  side  of  the  tree  bears  what  ratio  to  the 
average  growth  of  the  terminal  twigs  on  the  same 
side? 

2.  What  is   the   ratio  of  the  average  growth  of 
the  twigs  from  the  lateral  buds  on  the  south  side 
of  the   tree   to  the  average  growth  from  the  ter- 
minal buds  on  the  same  side? 

3.  What  is  the   ratio  of  the  average  growth  of 
the  lateral  twigs  on  the  east  side  of  the  tree  to  the 
average  growth  of  the  terminal  twigs  on  the  same 
side? 

4.  What  is  the  ratio  of  the  average  growth  of 
lateral  twigs   on  the   west  side  of  the  tree  to  the 
average  growth  of   the  terminal  twigs  on  the  same 
side? 

5.  What  is   the  ratio  of  the  average  length  of 
the  terminal  twigs  on  the  north  side  of  the  tree  to 
the  average   length  of  the  terminal  twigs  on  the 
south  side? 

6.  What   is   the   ratio  of  the  average  length  of 
the  lateral  twigs  on  the  north  side  of  the  tree  to 
the  average   length   of   the  lateral  twigs   on    the 
south  side? 

7.  What  is   the  ratio  of  the  average  length  of 
the   terminal   twigs  on  the  east  side  of  the  tree  to 
the  average  length  of  the   terminal  twigs  on  the 
west  side  ? 

>       ,  8.  What   is  the   ratio  of  the  average  length  of 
the  lateral  twigs  on  the  east  side  of  the  tree  to  the 


October]  BOTANY,  87 

average  length  of  the   lateral    twigs    on  the  west 
side? 

9.  What   is   the   ratio  of   the   average  length  of 
the  lateral  growths  of  the  entire  tree  to  the  average 
length  of  the  terminal  growths? 

10.  What  is   the  ratio  of  the  average  length  of 
the  terminal  growths  on  the  north  side  of  the  tree 
to  the   average  length  of  the  terminal  growths  on 
the  east  side  ?     On  the  west  side  ? 

11.  What  is  the  ratio  of  the  average  length  of 
the  lateral   growths  on  the  north  side  of  the  tree 
to  the  average  length  of  the  lateral  growths  on  the 
east  side?     On  the  west  side? 

12.  What  is  the  ratio  of  the  average  length  of 
the  terminal  twigs  on  the  south  side  of  the  tree  to 
the  average   length  of  the  terminal  twigs  on  the 
east  side?     On  the  west  side ? 

13.  What  is  the  ratio  of  the  average  length  of 
the  lateral  twigs  on   the  south  side  of  the  tree  to 
the  average  length  of  the  lateral  twigs  .on  the  east 
side?     On  the  west  side? 

14.  What  is  the  ratio  of  the  greatest  horizontal 
distance  from  the  trunk  through  which  any  branch 
extends    on    the    north    side  of    the  tree    to    that 
through   which   any   branch  extends  on  the  south 
side? 

15.  What  is  the  ratio  of   the  greatest  horizontal 
distance  from  the  trunk  through  which  any  branch 
extends  on  the  east  side  of  the  tree  to  that  through 
which  any  branch  extends  on  the  west  side? 

1C).  What  is  the  ratio  of  the  greatest  horizontal 
distance  from  the  trunk  through  which  any  branch 


I  NUMBER  WORK.  [October 

extends  on  the  north  side  of  the  tree  to  that 
through  which  any  branch  extends  on  the  east 
side  ?  On  the  west  side  ? 

17.  What  is  the  ratio  of  the  greatest  horizontal 
distance  through  which  any  branch  extends  on  the 
south  side  of  the  tree  to  that  through  which  any 
branch   extends   on   the   east  side?     On  the  west 
side? 

B.     The  preceding  year. — (Note  whether  or  not  the 
tree  has  reached  its  maturity.} 

18.  What  is  the  ratio  of  the  average  terminal 
growth  of  the  twigs  on  each  side  of  the  tree  to  the 
average  growth  of  terminal  twigs  for  the  present 
year  ? 

19.  What   is   the    ratio  of   the  average   lateral 
growth  of  the  twigs  on  each  side  of  the  tree  to  the 
average  lateral  growth  for  the  present  year? 

20.  The  average  terminal  growth  for  the  entire 
tree    bears  what   ratio    to    the    average    terminal 
growth  for  the  present  year? 

21.  The  average  lateral  growth  for  the   entire 
tree  bears  what  ratio  to  the  average  lateral  growth 
of  the  entire  tree  for  the  present  year? 

22.  The  average  terminal   growth   of   the    oak 
bears  what  ratio  to  the  average  terminal  growth 
of  the  maple?    The  ash?    The  willow?    The  box- 
elder?     The  elm? 

23.  The  average  lateral  growth  of  the  oak  bears 
what  ratio  to  the   average  lateral  growth   of  the 
maple?     The  ash?    The  willow?     The  box-elder? 
The  elm? 


October]  BOTANY.  89 

IV.     PERCENTAGE. 
A.     The  present  year. 

1.  The   average  growth  of  the   twigs  from  the 
lateral  buds  on  the  north  side  of  the  tree  equals 
what    per  cent  of  the  average   growth   from    the 
terminal  buds  on  the  same  side  ? 

2.  The  average  growth  of  the  twigs  from  the 
lateral  buds  on  the  south  side  of  the  tree  equals 
what   per   cent  of  the  average   growth   from   the 
terminal  buds  on  the  same  side  ? 

3.  The  average  growth  of  the  twigs  from  the 
lateral  buds  on  the  east  side  of    the  tree  equals 
what  per   cent  of  the    average  growth   from   the 
terminal  buds  on  the  same  side? 

4.  The  average  growth  of  the  twigs  from  the 
lateral  buds  on  the  west  side  of  the  tree  equals 
what  per  cent  of   the  average  growth    from   the 
terminal  buds  on  the  same  side? 

5.  The  average  terminal  growth  on  the    north 
side  of  the  tree  equals  what  per  cent  of  the  aver- 
age terminal  growth  on  the  south  side? 

6.  The  average  lateral  growth  on  the  north  side 
of   the  tree  equals  what  per  cent  of  the  average 
lateral  growth  011  the  south  side  ? 

7.  The  average  terminal  growth  on  the  east  side 
of  the  tree  equals  what  per  cent  of  the  terminal 
growth  on  the  west  side? 

8.  The  average  lateral  growth  on  the  east  side 
of   the   tree  equals  what  per  cent  of  the  average 
lateral  growth  on  the  west  side? 

9.  The  average  lateral  growth  over  the  entire 
tree  equals  what  per  cent  of  the  terminal  growth  ? 


90  NUMBER  WORK.  [October 

10.  The  average  terminal  growth  on  the  north 
side  of  the  tree  equals  what  per  cent  of  the  aver- 
age terminal  growth  on  the  east  side  ?    Of  that  on 
the  west  side  ? 

11.  The   average   lateral  growth   on   the  north 
side  of  the  tree  equals  what  per  cent  of  the  average 
lateral  growth   on  the  east  side?     Of  that  on  the 
west  side? 

12.  The  average  terminal  growth  on  the  south 
side  of  the  tree  equals  what  per  cent  of  the  aver- 
age terminal  growth  on  the  east  side  ?     Of  that  on 
the  west  side? 

13.  The   average   lateral  growth  on  the  south 
side  of  the  tree  equals  what  per  cent  of  the  aver- 
age lateral  growth  on  the  east  side  ?     Of  that  on 
the  west  side? 

14.  The  greatest   horizontal    distance    through 
which  any  branch  extends  on  the  north  side  of  the 
tree  equals  what  per  cent  of  the  distance  through 
which  any  branch  extends  on  the  south  side?   The 
east  side?     The  west  side? 

15.  The  greatest   horizontal    distance    through 
which  any  branch  extends  on  the  east  side  of  the 
tree  equals  what  per  cent  of  the  distance  through 
which  any  branch  extends  on  the  west  side?     The 
south  side  ? 

16.  The   greatest    horizontal   distance    through 
which  any  branch  extends  from  the  trunk  on  the 
south  side  of  the  tree  equals  what  per  cent  of  that 
through   which  any   branch   extends   on  the  west 
side? 


October]  BOTANY.  91 

B.     The  preceding  year. —  (Note  whether  or  not  the 
tree  has  reached  maturity.) 

17.  The  average  terminal  growth  of  the  twigs 
on  each  side  of  the  tree  equals  what  per  cent  of 
the  average  terminal  growth  for  the  present  year? 

18.  The  average  lateral  growth  on  each  side  of 
the  tree  equals  what  percent  of  the  average  lateral 
growth  for  the  present  year? 

19.  The  average  terminal  growth  of  the  entire 
tree  equals  what  per  cent  of  the  average  terminal 
growth  for  the  present  year? 

20.  The  average  growth  of  the  lateral  twigs  over 
the  entire  tree  equals  what  per  cent  of  the  average 
growth  of  the  lateral  twigs  for  the  present  year  ? 

21.  The  average  growth  of  the  lateral  twigs 
over  the   entire   tree  equals  what  per  cent  of  the 
average  growth  of  the  terminal  twigs? 

22.  The  average  terminal  growth  of    the  oak 
equals    what    per   cent   of    the    average    terminal 
growth  of  the  maple  ?     Of  the  ash  ?     Of  the  wil- 
low ?     Of  the  box-elder  ?     Of  the  elm  ? 

23.  The  average  lateral  growth  of  the  oak  equals 
what  per  cent  of  the  average  lateral  growth  of  the 
maple?     Of  the    ash?     Of  the    willow?      Of  the 
box-elder?     Of  the  elm? 


THE  DISTRIBUTION  OF  SEEDS. 

The  distribution  of  seeds  is  a  most  interesting  and 
suggestive  phase  of  plant  life.  It  is  the  design,  in 
the  following  study,  to  give  the  pupils  from  this 
standpoint  a  glimpse  of  the  relation  of  the  plant  to 
its  environment,  and  to  show  something  of  that 
great  flexibility  which  the  organism  displays  in  adapt- 
ing itself  to  its  surroundings.  In  as  large  a  collection 
as  it  is  possible  for  the  pupils  to  make  conveniently,  it 
is  suggested  that  they  look  for  the  following  classes: 

1.  The   seeds  that   may    be    distributed    by    the 
wind  by  means  of  either  sails,  wings,  or  pappus. 

2.  The  seeds  that  may  be  distributed  by  animals 
after  having  been  eaten  by  them  along  with  some 
other  part  of  the  fruit. 

3.  The  seeds  that  are  eaten  as  food  when  ripe. 

4.  The  seeds  that  are  stored  as  food  for  future  use. 

5.  The  seeds  that  may  be  distributed  by  being 
carried  about  in  the  hair  or  other  covering  of  animals. 

6.  The  seeds  that  are  distributed  by  some  struct- 
ural contrivance  of  their  own;    as,  in  the  case  of  the 
touch-me-not,  by  an  elastic  pod. 

7 .  The  seeds  with  no  evident  means  of  distribution . 

8.  The  seeds  about  which  the  pupil  is  uncertain. 

PROBLEMS. 
I.     WHOLE  NUMBERS. 

1.  How  many  of  your  fruits  are  used  as  food  by 
one  or  more  different  kinds  of  animals? 
92 


October] 


BOTANY. 


93 


2.  How   many  of  your   fruits  are  not  eaten  by 
any  animal  that  you  know? 

3.  How  many  of  your  fruits  are  devoured  whole 
by  animals? 

4.  How  many  of  your  fruits  are  eaten  for  the 
seeds   which  they   contain?     In  how  many  kinds 
are  the  seeds  totally  destroyed  by  the  animals? 

5.  In  how  many  cases  are  the  seeds  devoured 
incidentally  along  with   some  other  part  of    the 
fruit? 

of    your 


many 


fruits   are   eaten 


by 
by 
by 

all 


6.  How 

insects  ? 

7.  How    many   of    your    fruits   are   eaten 
birds? 

8.  How    many    of    your   fruits    are   eaten 
mammals  ? 

9.  How  many  of  your  fruits  are  eaten  by 
three  of  the  above  classes  of  animals? 

10.  How  many  different  kinds  have  you  that 
are  stored  up  by  animals  for  winter  food? 

11.  How  many  different  kinds  can  not  be  stored 
up  for  winter  food  ? 

12.  How   many  different   kinds  of   fruits  have 
you  that  are  nor  sought  by  animals  for  food? 

13.  How   many   different   kinds  of  fruits   have 
you  found  that  are  carried  about  in  the  wool,  fur, 
or  hair  of  animals  being  held  by  hooks  or  prickles? 

14.  How  many  of  those  that  are  carried  about 
in  the  coverings  of  animals  are  used  as  food  by 
animals  ? 

15.  How  many  fruits  have  you  collected   that 
have  been  stung  by  insects? 


94  NUMBER  WORK.  [October 

16.  How  many   fruits  have  you    collected  that 
have  no  injuries  whatever? 

17.  How   many  fruits  have   you  collected  that 
are  provided  with  any  means  of  protection  against 
animal  depredations? 

18.  How  many  fruits  have  you  found  that  are 
distributed  by  the  wind? 

19.  How  many  fruits  have  you  found  that  are 
distributed   by  the    wind  that   are  eaten   by  ani- 
mals?    How  many  are  in  no  wise  interfered  with 
by  animals? 

20.  How  many  fruits  have  you  found  provided 
with  wings  or  sails?     How  many  have  no  append- 
ages to  assist  directly  in  distribution? 

21.  Which  is  the  greater,  and  how  much,  the 
number  of  fruits  in  your  collection  used  in  some 
way  by  animals,  or  the  number  not  so  used  ? 

22.  How  many  kinds  of   fruits  have  you  that 
are  thrown  from  the  pod  by  some  means  when 
ripe  ? 

23.  How  many  different  kinds  of  fruits  can  you 
find  that  will  float  in  water? 

24.  How  many  different  kinds  of  fruits  can  you 
find  that  will  roll  on  sloping  ground? 

II.     FRACTIONS. 

1.  What   part  of  the   entire   number  of   fruits 
that    you    have   gathered  is  used  by   animals  as 
food? 

2.  What  part  of    the   entire  number  of  fruits 
that  you  have  gathered  is  not  so  used? 

3.  What  part  of   the  entire   number  of  fruits 
that  you  have  gathered  is  devoured  whole? 


October]  BOTAXY  95 

4.  What   part   of  the    entire    number  of  fruits 
that  you  have  gathered  is  devoured  for  the  seeds 
they  contain?      What  part   is  entirely  destroyed 
when  eaten? 

5.  What   part  of    the   entire  number  of  fruits 
that   you    have  gathered   is  eaten  for  the  pulp  or 
fleshy  portion? 

6.  What  part   of  the   whole   number   of   fruits 
that  you  have  gathered  is  eaten  by  insects? 

7.  What  part  of    the   entire    number  of  fruits 
that  you  have  gathered  is  eaten  by  birds? 

8.  What   part  of   the  entire  number  of   fruits 
that  you  have  gathered  is  eaten  by  mammals? 

9.  What  part  of    the   entire    number  of  fruits 
that  you  have  gathered  is  eaten  by  all  three  classes 
of  animals  named  above  ? 

10.  What  part  of  the  entire   number  of  fruits 
that  you  have  gathered   is  stored  up  for  winter 
food  by  animals? 

11.  What  part  of  the  entire   number  of  fruits 
that  you   have  gathered  can  not  be  so  stored  for 
food? 

12.  What  part  of  the  entire  number  of  fruits 
collected  are  carried  about  in  animal  coverings  by 
means  of  hooks  and  prickles? 

13.  What  part  of  the   whole  number  of  fruits 
provided  with  hooks  and  prickles  is  used  for  food  ? 

14.  What  part  of  the  entire  number  of  fruits  in 
your  collection  has  been  stung  by  insects? 

15.  What  part  of  the  entire  number  of  fruits 
collected  have  not   been  injured  in  any  way  what- 
ever by  animals? 


96  NUMBER  WORK.  [October 

16.  What  part  of  the  whole  number  of  fruits  in 
your  collection   is   provided  with   some  means  of 
defense  against  animal  depredations? 

17.  What  part   of  the   whole  number  of  fruits 
collected  is  distributed  by  the  wind  ? 

18.  What  part  of  the  entire  number  of   fruits 
collected  is  provided  with   sails  or  wings?     What 
part  is  without  such  appendages  ? 

19.  Wliat  part  of  the  number  of  fruits  distrib- 
uted by  the  wind  is  eaten  by  animals? 

20.  What  part  of  the  entire  number  of  fruits 
collected  is  thrown   from  the  pod,  by  some  means, 
when  ripe? 

21.  What  part  of  the  entire  number  of  fruits 
collected  will  roll  on  sloping  ground  ? 

22.  What   part  of  the  entire  number  of  fruits 
collected  will  float  on  water? 

III.     EATIO. 

1.  In   the   whole    number   of   fruits    you    have 
gathered,  what  is  the  ratio  of  the  number  used  by 
animals  for  food  to  the  number  not  so  used  ? 

2.  What  is  the  ratio  of  the  number  of  fruits 
devoured  whole  to  the  number  of  those  that  are 
broken  up  while  being  eaten? 

3.  What  is  the   ratio  of  the  number  of  fruits 
that  are  eaten  for  the  seeds  they  contain  to  the 
number  eaten  for  the  pulp?     What  is  the  ratio  of 
those  in  which  the  seeds  are  destroyed  when  eaten 
to  the  entire  number  ? 

4.  What  ratio  does  the  number  of  fruits  eaten 
by  insects  bear  to  the  entire  number  collected? 


October]  BOTANY.  97 

5.  What  ratio  does  the  number  of  fruits  eaten 
by  birds  bear  to  the  entire  number  collected? 

6.  What  ratio  does  the  number  of  fruits  eaten 
by  mammals  bear  to  the  entire  number  collected? 

7.  What  is  the   ratio  of  the  number  of  fruits 
eaten  by  insects  alone  to  the  number  of  fruits  eaten 
by  birds  alone? 

8.  What  is   the   ratio  of  the  number  of  fruits 
that  are  stored  for  food  to  the  number  not  so  stored  ? 

9  What  is  the  ratio  of  the  number  of  fruits  and 
seeds  that  may  be  carried  about  in  the  coverings  of 
animals  to  the  number  not  thus  distributed  ?  What 
is  the  ratio  to  the  entire  number  collected? 

10.  What  is  the  ratio  of  the  number  of  the  fruits 
provided  with  hooks  and  prickles  that  are  used  as 
food  to  those  of  the  same  kind  not  so  used? 

11.  What  is  the  ratio   of  the   number  of  fruits 
which  you  have  that  have  been  stung  by  insects  to 
the  number  that  are  not  so  injured? 

12.  What  ratio  does  the  number  of  fruits  that 
are  provided  with  means  of  defense  against  animal 
depredations  bear  to  the  number  that  are  not  so 
provided  ? 

13.  What  is  the  ratio  of  the  number  of  fruits 
that  you  can  find  that  are  distributed  by  the  wind 
to  the  number  dependent  upon  animals  for  distri- 
bution ? 

14.  What  is  the  ratio  of  the  number  of  fruits 
provided  with  sails  or  wings  to  the  number  not  so 
provided  ? 

15.  What  ratio   does  the  number  of  fruits  col- 
lected which  have  no  obvious  means  for  distribution 


98  NUMBER  WORK.  [October 

bear  to  the  number  provided  with  some  means  for 
this  purpose? 

16.  What  is  the  ratio  of  the  number  of  kinds  of 
seeds  thrown  from  the  pod  when  ripe  to  the  whole 
number  collected? 

17.  What  is  the   ratio  of  the  number  that  will 
roll  on  sloping  ground  to  the  entire  number  col- 
lected? 

18.  What  is  the  ratio  of  the  number  that  will 
float  011  water  to  the  entire  number? 

IV.     PERCENTAGE. 

1.  What   per  cent  of  the  fruits   that  you  have 
gathered  are  used  as  food  by  wild  animals  ? 

2.  What   per  cent  of  the   fruits  that  you  have 
gathered  are  not  used  as  food  by  wild  animals? 

3.  What  per  cent  of  the  fruits  that  you  have 
collected  are  devoured  whole 

4.  What   per  cent  of  the   fruits   that  you  have 
gathered  are  devoured  for  the  seeds  they  contain  ? 
What   per   cent   have   the  seeds  destroyed  when 
eaten  ? 

5.  What  per  cent  of  the  fruits  that  you  have 
gathered  are  devoured  for  the  pulpy  part? 

6.  What  per  cent  of  the  fruits  that  you  have 
gathered  are  eaten  by  insects  ?     What  per  cent  of 
the  fruits  that  you  have  gathered  are  not  touched 
by  insects? 

7.  What  per  cent  of  the  fruits   that  you  have 
gathered  are  eaten  by  birds?     What  per  cent  are 
not  eaten  by  birds  ? 

8.  What  per  cent  of  the  fruits  that  you   have 
gathered  are  eaten  by  mammals?     What  per  cent 
are  not  eaten  by  mammals? 


October]  BOTANY.  99 

1).  What  per  cent  of  the  fruits  that  you  have 
gathered  are  eaten  in  common  by  all  the  above- 
mentioned  classes  of  animals? 

10.  What  per  cent  of  the  fruits  with  which  you 
are  familiar  are  stored  by  animals  as  winter  food? 
What  per  cent  are  not  so  stored? 

11.  What   per  cent  of  the  entire   number   col- 
lected are  carried  about  in  the  coverings  of  animals 
by  hooks  or  prickles?     What  per  cent  can  not  be 
so  carried? 

12.  What  per  cent  of  the  number  of  fruits  pro- 
vided with  hooks  and  prickles  are  used  as  food  by 
wild  animals  ?     What  per  cent  are  not  so  used  ? 

13.  What  per  cent  of  the  fruits  collected  have 
been  stung  by  insects? 

14.  What  per  cent  of  the  fruits  collected  have 
sustained  no  injuries  from  animals? 

15.  What  per  cent  of  the   fruits  collected  are 
provided    with    some    means    of    defense    against 
animal  depredations? 

16.  What  per  cent   of   the  entire  number  col- 
lected are  distributed  by  the  wind? 

17.  What    per  cent   of    the   entire  number  are 
provided  with  sails  or  wings? 

18.  What  per  cent  of  the  fruits  collected  are  not 
provided  with  any  appendages  which  aid  directly 
in  their  distribution  ? 

19.  What  per  cent  of  the  entire  collection  are 
thrown  from  the  pod  when  ripe? 

20.  The  number  that  will  roll  on  sloping  ground 
is  what  per  cent  of  the  entire  collection  ? 

21.  The  number  that  will  float  on.  water  is  what 
per  cent  of  the  entire  collection? 


PHYSICS. 


EBULLITION. 

The  following  problems  are  to  be  used  in  showing 
how  the  boiling  point  is  affected  by  the  salts  in  solu- 
tion and  also,  that  the  boiling  point  varies  with  the 
nature  of  the  liquid.  The  experiments  may  be  varied 
by  using  distilled  water,  hydrant  water,  spring  water, 
and  water  containing  different  substances  dissolved 
in  varying  amounts  up  to  the  point  of  saturation. 
The  boiling  point  of  pure  water  at  the  sea  level 
with  the  barometer  at  thirty  inches  is  212°  Fahren- 
heit. 

PROBLEMS. 
I.     WHOLE  NUMBERS. 

1.  What  is  the   difference  between  the  boiling 
point  of  pure  distilled  water  and  that  of   hydrant 
water?     Hydrant  water  and  well  or  spring  water? 
Distilled  water  and  spring  water? 

2.  What  is  the   difference,  in  degrees,  between 
the  boiling  point  of  distilled  water  and  the  boiling 
point  of  alcohol? 

3.  In  ninety  cubic  centimeters  of  distilled  water, 
dissolve  ten  grams  of  salt;  how   much   does  this 
raise  the  boiling  point? 

4.  In  ninety  cubic  centimeters  of  distilled  water, 

100 


Ortoberj  PHYSICS.  101 

dissolve   ten  grams  of  alum;    how   much  does   it 
raise  the  boiling  point? 

5.  What  is  the  difference  between  the   boiling 
point  of  a  saturated  salt  solution  and  the  boiling 
point  of  pure  water? 

6.  What  is  the   difference   between  the  boiling 
point  of  a  saturated  alum  solution  and  the  boiling 
point  of  pure  water? 

7.  What  is  the  difference   between  the  boiling 
point  at  your  elevation   and  the  boiling  point  at 
sea  level? 

II.     FRACTIONS. 

1.  The  boiling  point,  in  degrees,  of  pure  water 
equals  what  part  of  the  boiling  point  of  hydrant 
water?     Spring  water?     Well  water? 

2.  The    boiling   point,    in    degrees,    of  alcohol 
equals  what  part  of  the  boiling  point  of  pure  water? 

3.  The  boiling  point,  in  degrees,  of  pure  water 
equals  what  part   of  the  boiling  point  of  ninety 
cubic  centimeters  of  water  in  which  ten  grams  of 
salt  are  dissolved?       Twenty  grams  of  salt? 

4.  The  boiling  point,  in  degrees,  of  pure  water 
equals  what  part  of  that   of  ninety   cubic  centi- 
meters of  water  in  which  ten  grams  of  alum  have 
been  dissolved?     Twenty  grams? 

5.  The  boiling  point,  in  degrees,  of  pure  water 
equals  what  part  of  the  boiling  point  of  a  saturated 
salt  solution  V 

6.  The  boiling  point,  in  degrees,  of  pure  water 
equals    what  part  of    the  boiling  point  of  a  satu- 
rated alum  solution? 

7.  The  boiling  point,  in  degrees,  at  your  elevation 


102  NUMBER  WORK.  [October 

equals    what    part  of    the    boiling    point   at   sea 
level? 

III.  KATIO. 

1.  What  is  the  ratio  of  the  boiling  point  of  pure 
water,  expressed  in  degrees,  to  the  boiling  point  of 
hydrant  water?     To  that  of  spring  water? 

2.  What  is  the  ratio  of  the  boiling  point  of  pure 
water,  expressed  in  degrees,  at   your  altitude  to 
the  boiling  point  at  the  sea  level? 

3.  What    is    the     ratio    of    the    boiling    point, 
expressed   in   degrees,   of   alcohol    to   the   boiling 
point  of  pure  water? 

4.  What  is  the  ratio  of  the  boiling  point  of  pure 
water,  expressed  in  degrees,  to  the  boiling  point  of 
ninety  cubic  centimeters  of  distilled  water  with 
ten  grams,  of  salt  dissolved  in  it? 

5.  What  is  the  ratio  of  the  boiling  point  of  pure 
water,  expressed   in    degrees,    to    that    of    ninety 
cubic    centimeters    of    distilled    water,    with    ten 
grams  of  alum  dissolved  in  it  ? 

6.  What  is  the  ratio  of  the  boiling  point  of  dis- 
tilled water,  expressed  in  degrees,  to   the  boiling 
point  of  a  saturated  salt  solution  ? 

7.  What  is  the  ratio  of  the  boiling  point  of  dis- 
tilled water,  expressed  in  degrees,  to  the  boiling 
point  of  a  saturated  alum  solution? 

IV.  PERCENTAGE. 

1 .  The  boiling  point  of  distilled  water,  expressed 
in  degrees,  equals  what  per  cent  of  the  boiling 
point  of  hydrant  water?  Spring  water?  Well 
water? 


October]  PHYSICS.  103 

2.  The  boiling  point  of   pure  water,  expressed 
in  degrees,  at  your  altitude  equals  what  per  cent 
of  the  boiling  point  at  sea  level? 

3.  The    boiling    point  of   alcohol,  expressed  in 
degrees,  equals  what  per  cent  of  the  boiling  point 
of  pure  water? 

4.  The  boiling  point  of  pure  water,  expressed 
in   degrees,  equals  what   per  cent  of    the  boiling 
point  of  a  ten  per  cent  salt  solution  ? 

5.  The  boiling  point  of  distilled  water,  expressed 
in  degrees,   equals  what  per  cent  of    the  boiling 
point  of   a  ten  per  cent  alum  solution  ? 

6.  The  boiling    point  of  pure  water,  expressed 
in  degrees,   equals  what   per  cent  of  the   boiling 
point  of  a  saturated  salt  solution? 

7.  The  boiling  point  of   pure  water,  expressed 
in  degrees,  equals  what    per  cent  of  the  boiling 
point  of  a  saturated  alum  solution? 


METEOROLOGY. 


I.     WHOLE  NUMBERS. 
A.     Temperature. 

1.  What  is  the  average  reading  of  the  thermom- 
eter for  October? 

2.  What  was  the  greatest  range  in  the  reading 
of  the  thermometer  during  the  month? 

3.  What  was  the  average  reading    of  the  ther- 
mometer for  the  first  week?    Second  week?    Third 
week?     Fourth  week? 

4.  What  is  the  greatest  difference  between  the 
average  reading  of  the  thermometer  for  any  two 
weeks? 

5.  What  is  the  difference  between     the  lowest 
reading  of   the   thermometer  in  October  and  the 
lowest  reading  in  September? 

6.  What  is  the  difference  between  the  highest 
reading   of   the  thermometer  in  October  and  the 
highest  reading  in  September? 

7.  What   is   the   difference  between  the  average 
reading  of   the  thermometer  in  October  and  the 
average  reading  for  September? 

8.  What  is   the  difference,  in  degrees,  between 
the  greatest  range  of  temperature  in  October  and 
the  greatest  range  in  September? 

104 


October]  METEOROLOGY.  105 

B.  Barometer. 

9.  What  is  the  difference  between  the  highest 
and  the  lowest  barometric  reading  for  October? 

10.  What  is  the  average  high  I  of  the  barometric 
column  for  October? 

11.  What  is  the  average  hight  of  the  barometric 
column  for  the  first  week?     The    second    week? 
The  third  week?     The  fourth  week? 

12.  What  is  the  difference  between  the  average 
hight  of   the   barometric  column  for  October  and 
the  average  hight  for  September? 

13.  What  is  the  difference  between  the  greatest 
barometric    range    for    October    and    the  greatest 
range  for  September? 

C.  Rainy,  Cloudy,  and  Clear  Days. 

14.  How  many   rainy   days  in  October?     How 
many  days  without   rain?     At  the  same  rate  how 
many  of  each  would  there  be  in  a  year? 

15.  Which  month   had  the  greater  number  of 
rainy  days,  and  how  much,  October  or  September? 

16.  Which  month   had   the   greater  number  of 
days    without    rain,   and    how    much,   October  or 
September  ? 

B.     RainfalL 

17.  What  was  the  total  rainfall  for  October? 

18.  What    was    the    average    rainfall    for  each 
rainy  day  in  October? 

19.  What  was  the  average  daily  rainfall  for  the 
month  ? 

20.  At  the   October   rate,    what   would   be    the 
total  rainfall  for  a  year  ? 


106  NUMBER  WORK.  [October 

21.  Which   had   the  greater   rainfall,   and  how 
much,  October  or  September? 

22.  What  was  the  average  rainfall  for  the  two 
months? 

23.  What    was    the   average    rainfall    for   each 
rainy  day  during  the  two  months? 

2-t.  What  was  the  daily  average  rainfall  for  the 
two  months? 

25.  Which  was  greater,  and  how  much,  the 
number  of  clear  days,  or  the  number  of  cloudy 
days  in  October? 

20.  What  was  the  daily  average  of  rainfall  for 
each  cloudy  day  in  October? 

27.  Which  was  the  greater,  and  how  much,  the 
average  rainfall  for  the  cloudy  days  of  October  or 
for  the  cloudy  days  of  September? 

28.  At  the  October  rate,  how  many  days  of  the 
year  would  be  cloudy? 

E.     Dew,  Frost,  and  Fogs. 

29.  How  many  dewy  mornings  in  October? 

30.  How  many  mornings  with  frost? 

31.  Which    month  had  the  greater  number  of 
dews,  and  how  much,  October  or  September?    The 
greater  number  of  frosts? 

II.     FRACTIONS. 
A.     Temperature. 

1.  The  average  reading  of  the  thermometer  for 
the  month  equals  what  part  of  the  highest  reading 
for  the  month?     Of  the  lowest? 

2.  The  average  reading  of  the  thermometer  for 
the  month  equals  what  part  of  the  average  reading 


October]  METEOROLOGY.  107 

for  the  first  week?     The  second  week?     The  third 
week?     The  fourth  week  ? 

3.  The  average  reading   of  the  thermometer  for 
October  is   what  part  of  the  average  reading  for 
September? 

4.  The  highest  reading  of   the  thermometer  for 
October  equals  what  part  of  the  highest  reading 
for  September? 

5.  The  lowest  reading  of  the  thermometer  for 
October  equals   what  part   of   the  lowest  reading 
for  September? 

6.  The  greatest    range  in  degrees   of  the  tem- 
perature in  October  equals  what  part  of  the  great- 
est range  in  September? 

B.     Barometer. 

7.  The  average  hight  of  the  barometer  for  Octo- 
ber equals  what  part  of   the  highest  barometer? 
Of  the  lowest? 

8.  The  average  hight  of  the  barometer  for  Octo- 
ber equals  what    part  of    the    average   hight    for 
September? 

9.  The  greatest  range  in  the  barometric  reading 
for  October  equals  what  part  of  the  greatest  range 
for  September? 

10.  The  average  hight  of   the  barometer  for  the 
rainy  days  during  the  month  equals  what  part  of 
the  average  hight  for  the  clear  days  ? 

11.  The  average  hight  of  the  barometer  for  the 
rniny  days  equals  what  part  of   the  average  hight 
for  the  cloudy  days  without  rain? 

12.  The  average  hight  of  the  barometer  for  the 
rainy  days  in  October  equals  what  part  of  the  aver- 
age   hight  for  the  rainy  days  in  September? 


108  NUMBER  WORK.  [October 

13.  The  average  hight  of  the  barometer  for  the 
clear  days  in  October  equals  what  part  of  the  aver- 
age hight  for  the  clear  days  in  September? 

C.  Rainy,  Cloudy,  and  Clear  Days. 

14.  The    number    of    rainy    days    for    October 
equals    what    part    of    the    entire    month?       The 
cloudy  days  equal  what  part  of  the  month  ? 

15.  The  number  of  rainy  days  equals  what  part 
of  the  number  of  cloudy  days  in  October? 

16.  The  number  of  rainy  days  equals  what  part 
of  the  number  of  clear  days  in  October? 

17.  The    number   of    rainy    days    for    October 
equals  what  part  of   the  number  of  rainy  days  for 
September? 

18.  The    number    of    cloudy    days    in    October 
equals  what  part  of  the  number  of  cloudy  days  in 
September? 

19.  The  number  of  cloudy  days  without  rain  in 
October  equals  what  part  of  the  number  of  cloudy 
days  without  rain  in  September? 

20.  The  number  of  clear  days  in  October  equals 
what  part  of  the  number  of  clear  days  in  Septem- 
ber? 

21.  At   the   October  and   September  rate  what 
part  of  the   entire   year  would  be   rainy  ?     What 
part  of  the  year  would  be  cloudy  ? 

D.  Rainfall. 

22.  The  rainfall   for   October  equals  what  part 
of  the  rainfall  for  September? 

23.  The  average  rainfall  for  each   rainy  day  in 
October  equals  what  part  of  the  average  for  the 
rainy  days  in  September? 


October]  METEOROLOGY.  109 

24.  The  average  rainfall  for  the  cloudy  days  in 
October  equals   what   part   of  the  average  for  the 
cloudy  days  in  September? 

25.  What  part  of  the  total  rainfall  occurred  when 
the  barometer  was  below  the  average  hight  for  the 
month? 

26.  What  part   of  the    total    rainfall    occurred 
when   the   wind    was    blowing    in    the    prevailing 
direction  ? 

27.  What  part  of  the  rainfall  occurred  when  the 
temperature  was  below  the  monthly  average? 

E.     Dew  and  Frost. 

28.  The  number  of  mornings  with  dew  equals 
what  part  of  the  entire  month  ? 

29.  The  number  of  mornings  with  frost  equals 
what  part  of  the  entire  month  ? 

30.  The   number   of    mornings    witli    frost   in 
October  equals  what  part  of  the  number  in  Sep- 
tember? 

III.     RATIO. 

A.     Temperature. 

1.  What  is  the  ratio  of  the  lowest  reading  of  the 
thermometer  to  the  highest  reading  in  October? 

2.  What  is  the  ratio   of  the  average  reading  of 
the  thermometer  for  the  first  week  to  the  monthly 
average  ? 

3.  What  is  the  ratio  of  the  average  reading  of 
the  thermometer  for  the  second  week  to  the  aver- 
age reading  for  the  month  ?     Of  the  third  week  ? 
Of  the  fourth  week? 

4.  What  is  the  ratio  of  the  average  reading  of 


110  NUMBER  WORK.  [October 

the  thermometer  for  the  first  week  to  the  .average 
reading  for  the  last  week  of  the  month  ? 

5.  "What  is  the  ratio  of   the  average  reading  of 
the  thermometer  for  October  to  the  average  read- 

o 

ing  for  September? 

6.  What  is  the   ratio   of   the  greatest   range  of 
temperature  during   October  to  the  greatest  range 
during  September? 

7.  What  is  the  ratio  of  the  highest  reading  of 
the  thermometer  in  October  to  the  highest  reading 
in  September? 

8.  What  is  the  ratio  of  the  lowest  reading  of  the 
thermometer  in  October  to  the  lowest  reading  in 
September? 

13*     Barometer. 

9.  What  is  the  ratio  of  the   highest  barometric 
reading  to  the  lowest  reading  for  October? 

10.  What  is  the  ratio  of  the  average  barometric 

O 

reading  on.  the  rainy  days  to  the  average  reading 
on  the  clear  days  ? 

11.  What  is  the  ratio  of  the  average  barometric 
reading  on  the   rainy  days  to  the  average  reading 
on  the  cloudy  days  without  rain  ? 

12.  What  is  the  ratio  of  the  average  barometric 
reading  for  October   to   the  average  reading  for 
September? 

13.  What  is  the  ratio  of  the  greatest  range  of 
the  barometer  in  October  to  the  greatest  range  in 
September. 

14.  What  is  the  ratio  of  the  average  barometric 
reading  during  the  rainy  days   in   October  to  the 
average  reading  during  the  rainy  days  in  Septem- 
ber? 


October]  METEOROLOGY.  Ill 

C.  Rainy,  Cloudy  and  Clear  Days. 

15.  What  is   the  ratio  of   the   number  of    rainy 
days  to  the  number  of  cloudy  days  in  October? 

16.  What  is   the   ratio  of  the  number  of  rainy 
days  to  the  number  of  clear  days  in  October? 

17.  What  is  the  ratio  of   the  number  of  rainy 
days   in   October   to  the   number   of  cloudy  days 
without  rain? 

18.  What  is  the  ratio  of  the  number  of  cloudy 
days  in  October  to  the  number  of  clear  days  ? 

19.  What  is  the  ratio  of  the  number  of  rainy 
days  in  October  to  the   number  of  rainy  days  in 
September? 

20.  What  is  the  ratio  of  the  number  of  cloudy 
days  in  October  to  the  number   of   cloudy  days  in 
September? 

21.  What  is  the  ratio  of   the  number  of  cloudy 
days   without  rain  in   October  to  the  number  of 
cloudy  days  without  rain  in  September? 

22.  What  is  the  ratio   of  the   number  of   clear 
days  in  October  to  the   number  of  clear  days  in 
September  ? 

D.  fiainfalL 

23.  ^hat    is    the    ratio  of  the  rainfall  for  the 
first  week  to  the  rainfall  for  the  month  ?     Of   the 
second  week?    Of  the  third  week?    Of  the  fourth 
week? 

24.  What  is  the  ratio  of  the  daily  average  rain- 
fall for  the  rainy  days  to  the  daily  average  for  the 
entire  month? 

25.  What  is  the  ratio  of  the  daily  average  rain- 


112  NUMBER  WORK.  [October 

fall  for  the  rainy  days  to  the  daily  average  for  the 
entire  number  of  cloudy  days  in  the  month  ? 

26.  What  is  the   ratio  of   the  total  rainfall  in 
October  to  the  total  rainfall  for  September? 

27.  What  is  the  ratio  of  the  daily  average  rain- 
fall  for   the    rainy  days  in    October   to    that  for 
the  rainy  days  in  September? 

28.  What  is  the  ratio  of  the  daily  average  rain- 
fall for  the  cloudy  days  in  October  to  that  for  the 
cloudy  days  in  September? 

E.     Dew  and  Frost. 

29.  What  is  the  ratio  of  the  number  of  dews  to 
the  number  of  frosts  in  October? 

30.  What  is  the  ratio  of  the  number  of  dews  in 
October  to  the  number  in  September? 

31.  What  is  the  ratio  of  the  number  of  frosts  in 
October  to  the  number  in  September? 

IV.     PERCENTAGE. 
A.     Temperature. 

1.  The  lowest  reading  of  the  thermometer  in 
October  equals  what  per  cent  of  the  highest  read- 
ing? 

2.  The  average  reading  of  the  thermometer  for 
the  first  week  in  October  equals  what  per  cent  of 
the  monthly  average?     For  the  second  week?  For 
the  third  week?     For  the  fourth  week? 

3.  The  average  reading  of  the  thermometer  for 
the  first  week  equals  what  per  cent  of  that  for  the 
last  week? 

4.  The  average  reading  of  the  thermometer  for 
October  equals  what  per  cent  of  the  average  for 
September  ? 


October]  METEOROLOGY.  113 

5.  The  highest  reading  of  the  thermometer  for 
October  equals  what  per  cent  of  the  highest  read- 
ing for  September? 

6.  The  lowest  reading  of  the  thermometer  for 
October  equals  what  per  cent  of  the  lowest  read- 
ing for  September? 

7.  The  greatest  range  of  temperature  for  Octo- 
ber equals  what  per  cent  of  the  greatest  range  for 
September  ? 

B.  Barometer. 

8.  The  lowest  barometer  in  October  equals  what 
per  cent  of  the  highest  reading? 

9.  The  average  hight  of  the  barometer  for  the 
rainy  days  equals   what   per  cent   of   the  average 
hight  for  the  clear  days? 

10.  The  average  hight  of  the  barometer  for  the 
rainy   days   equals  what   per  cent  of  the  average 
hight  for  the  cloudy  days  without  rain  ? 

11.  The  average    hight  of   the  barometer  for 
October  equals  what  per  cent  of  the  average  hight 
for  September? 

12.  The    average    hight  of   the  barometer  for 
the  rainy  days  in  October  equals  what  per  cent  of 
the  average  hight  for  the   rainy   days  in  Septem- 
ber? 

13.  The  average  hight  of  the  barometer  for  the 
clear  days  in  October  equals  what  per  cent  of  the 
average  hight  for  September? 

14.  The  highest  barometric  reading  for  October 
equals  what  per  cent  of  the   highest  barometric 
reading  for  September? 


114  NUMBER  WORK.  [October 

C.  Rainy,  Cloudy,  and  Clear  Days. 

15.  The  number  of  rainy  days  equals  what  per 
cent  of  the  whole  month  ? 

16.  The   number  of   cloudy   days  equals  what 
per  cent  of   the   entire   month?     The   number  of 
clear  days? 

17.  The  number  of  rainy  days  equals  what   per 
cent  of  the  number  of  cloudy  days  ?    Of  the  num- 
ber of  clear  days? 

18.  The  number  of   cloudy  days   without   rain 
equals  what  per  cent  of  the  whole  number  of  cloudy 
days?     Of  the  entire  month ? 

19.  The  number  of  rainy  days  in  October  equals 
what   per  cent   of   the  number  of   rainy  days  in 
September? 

20.  The   number   of    cloudy   days    in    October 
equals  what  per  cent  of  the  number  of  cloudy  clays 
in  September? 

21.  The   number  of  cloudy   days  without  rain 
in  October- equals  what  per  cent  of  the  number  of 
cloudy  days  without  rain  in  September? 

22.  The  number  of  clear  days  in  October  equals 
what  per  cent  of  the  number  of  clear  days  in  Sep- 
tember? 

23.  At  the  October  and  September  rate  what 
per  cent  of  the  entire  year  would  be  rainy  ? 

D.  Rainfall. 

24.  The   rainfall   for  October  equals  what  per 
cent  of  the  rainfall  for  September? 

25.  The  average  rainfall  for  each  rainy  day  in 
October  equals  what  per  cent  of  the  average  for 
each  rainy  day  in  September? 


October]  METEOROLOGY.  115 

26.  The  average  daily  rainfall    for  the  entire 
month   of  October  equals  what  per  cent  of  the 
average  for  September? 

27.  The  average   daily   rainfall  for  the  cloudy 
days  in  October  equals  what  per  cent  of  the  aver- 
age for  the  cloudy  days  in  September? 

28.  What  per  cent  of  the  rainfall  occurred  when 
the  barometer  was  below  the  average  hight  ? 

29.  What  per  cent  of  the  rainfall  occurred  when 
the  prevailing  wind  for  the  month  was  blowing  ? 
E.     Dew  and  Frost. 

30.  The  number  of  mornings  with   dew  equals 
what  per  cent  of  the  entire  month  of  October  ? 

31.  The  number  of  mornings  with  frost  equals 
what  per  cent  of  the  entire  month  ? 

32.  The  frosty  mornings  in  October  equals  what 
per  cent  of  the  dewy  mornings  in  September? 


ASTRONOMY. 


VARIATION  IN  DAY'S    LENGTH  AND   POSI- 
TION OF  THE  SUN  ON  THE  MERIDIAN. 
I.     WHOLE  NUMBERS. 

1.  What  is  the  change  in  the  day's  length  dur- 
ing the  first  week?     During  the  second?     During 
the  third?     During  the  fourth? 

2.  What    was    the    total    change    in    the    day's 
length  for  the  entire  month  ? 

3.  How   many    minutes    did    the    day's    length 
vary  in  the  morning  during  the  first  week?     The 
second?     The  third?     The  fourth? 

4.  How    many    minutes    did   the    day's    length 
vary  in  the  morning  during  the  month  ? 

5.  How    many    minutes    did   the    day's    length 
vary  in  the  evening  during  the  first  week?    The 
second  ?     The  third  ?     The  fourth  ? 

6.  How    many    minutes    did    the    day's    length 
vary  in  the  evening  during  the  entire  month? 

7.  Which  is  greater  during  the  month,  and  how 
much,  the  variation  in  the  morning  or  the  varia- 
tion in  the  evening? 

8.  Which  is  greater,  and  how  much,  the  varia- 
tion during  the  first  week  or  the  variation  during 
the  last  week? 

9.  How   many  degrees  did  the   sun  change  on 

116 


October]  ASTRONOMY.  117 

the    meridian    during    the    month?      How    many 
degrees  each  week? 

10.  What  is  the  difference  between  the  length 
of  day  and  the  length  of  night  at  the  beginning 
of  the  month  ? 

11.  What  is  the  difference  between  the  length 
of    day  and  the  length  of    night  at  the  end  of  the 
month  ? 

12.  What  was  the  change,  and   how  much,  in 
the  length  of  the  day  from  the  first  of   September 
till  the  last  of   October? 

13.  What  is  the  difference  between  the  change 
in  day's  length  in  September  and  the  change  in 
October? 

14.  What  is  the  difference  between  the  change 
in  day's  length  in  the  first  week  in  September  and 
the  change  in  the  last  week  in  October? 

15.  Which    was    greater,    and    how    much,   the 
movement  of  the  sun  on  the  meridian  in  Septem- 
ber or  its  movement  on  the  meridian  in  October? 

16.  What  is  the  difference  between  the  amount 
of  the  sun's  movement  on  the  meridian  during  the 
first   week   in   September    and   the  amount  of    its 
movement  during  the  last  week  in  October?  . 

17.  What    is    the   difference   between   the   area 
of  the  shadow  cast  by  the  shadow-stick  during  the 
first    week    in    September    and    the    area    of    the 
shadow  cast  during  the  first  week  of  October? 

18.  What  is  the  difference  between  the  area  of 
the  shadow  cast  during  the  first  week  in  October 
and  the  area  of  the  shadow  cast  during  the  second 
week?     The  third  week?     The  fourth  week? 


118  NUMBER  WORK.  [October 

19.  What  is   the    difference    between    the   area 
of  the  shadow  cast  by  the  shadow-stick  during  the 
first  week  in  September  and  the  area  of    that  cast 
daring  the  last  week  in  October? 
II.     FRACTIONS. 

1.  What  part  of  the  day's  length  at  the  begin- 
ning of  the   month  was   lost  or  gained  during  the 
first    week?      During    the    second?     During   the 
third  ?     During  the  fourth  ? 

2.  What  part  of  the  day's  length  at  the  begin- 
ning of  the  month   was  lost  or  gained  during  the 
entire  month  ? 

3.  What  part  of  the  loss  or  gain  during  the  first 
week  in  the  month  occurred  in  the  morning?     The 
second    week?      The    third    week?      The    fourth 
week? 

4.  What  part  of  the   loss   or  gain  during   the 
first  week   occurred  in  the  evening?     The  second 
week?     The  third  week?     The  fourth  week? 

5.  The   loss   or   gain  'during  the   month  in  the 
morning  equals  what  part  of  the  loss  or  gain  dur- 
ing the  evening? 

6.  The  loss  or  gain  in   the  day's  length  during 
the   first   week  in   the   month  equals  what  part  of 
the  loss  or  gain  during  the  last  week  ? 

7  The  movement  of  the  sun  on  the  meridian 
during  the  first  week  in  the  month  equals  what 
part  of  the  movement  for  the  entire  month  ?  The 
second  week  ?  The  third  week  ?  The  fourth  week  ? 

8.  The  gain  or  loss  in  the  day's  length  during 
October  equals  what  part  of  the  gain  or  loss  dur- 
ing September? 


October]  ASTRONOMY.  119 

(->.  The  gain  or  loss  in  the  day's  length  during 
the  last  week  in  October  equals  what  part  of  that 
during  the  first  week  in  September? 

10.  The  gain  or  loss  in  the  day's  length  in  the 
morning   during  October  equals  what  part  of  the 
gain  or  loss  for  the  same  time  during  September? 

11.  The  gain  or  loss  in  the  day's  length  in  the 
evening  during  October  equals  what  part  of  the 
gain  or  loss  for  the  same  time  during  September? 

12.  The  morning   variation  in  the  day's  length 
during  the  last  week  in  October  equals  what  part 
of  the  morning  variation  the  first  week  in  Septem- 
ber? 

13.  The   evening  variation   in  the  day's  length 
during  the  last  week  in  October  equals  what  part 
of  the  evening  variation   during  the  first  week  in 
September? 

14.  The  change  of  the   sun's   position   on    the 
meridian  during  October  equals  what  part  of  the 
change  during  September? 

15.  The  change  of    the  sun's    position  on  the 
meridian  during  October  equals  what  part  of  the 
entire  change  since  September  first? 

16.  The  area  of  the  shadow  cast  by  the  shadow- 
stick  the  first  week  in  October  equals  what  part  of 
the  area  cast  the  last  week  ? 

17.  The  area  of  the  shadow  cast  the  first  week 
in  October  equals   what   part  of  the   area   of  the 
cross  section  of  the  si  ick  ? 

18.  The  area  of  the  shadow  cast  the  first  week 
in  September  equals  what  part  of  the  area  of  that 
cast  the  last  week  in  October? 


120  NUMBER  WORK.  [October 

III.     RATIO. 

1.  What  is  the  ratio  of  the  variation  in  the  day's 
length  during  the  first  week  in  October  to  that  for 
the  entire  month  ?     During  the  second?     During 
the  third?     During  the  fourth? 

2.  What  is  the  ratio  of  the  day's  length  at  tho 
beginning  of  the  month  to  the  length  at  the  end 
of  the  month? 

3.  What   is  the  ratio  of  the  morning  variation 
in  the  day's  length  during  the  first  week  to  the 
morning  variation  for  the  entire  month  ?     During 
the  second  week  ?     During  the  third  week  ?     Dur- 
ing the  fourth  week? 

4.  What  is  the  ratio  of  the  evening  variation  in 
the  day's  length  during  the  first  week  to  the  even- 
ing variation  for  the  entire  month  ?     During  the 
second  week?     During  the  third  week?     During 
the  fourth  week? 

5.  What  is  the  ratio  of  the  morning  variation 
in  the  day's  length  during  the  first  week  to  the 
evening  variation  for  the  same  time  ?     During  the 
second  week?     During  the  third  week?     During 
the  fourth  week? 

6.  What  is  the  ratio   of  the  morning   variation 
in  the  day's  length  during  the  month  to  the  even- 
ing variation  for  the  same  time? 

7.  The  number  of  degrees  through  which  the 
sun  moves  on  the  meridian  during  the  first  week 
bears  what  ratio  to  the  entire  number  of  degrees 
for  the  month?     During  the  second  week?     Dur- 
ing the  third  week?     During  the  fourth  week? 

8.  What  is  the  ratio  of  the  variation  in  the  day's 


October]  ASTRONOMY.  121 

length    during    October    to    the  variation   during 
September? 

1).  What  is  the  ratio  of  the  variation  in  the  day's 
length  during  the  last  week  in  October  to  the 
variation  during  the  first  week  in  September? 

10.  What  is  the  ratio  of  the  morning  variation 
in  the  day's  length  during  October  to  the  morning 
variation  for  September? 

11.  What  is  the  ratio  of  the  evening  variation 
in  the  day's  length  during  October  to  the  evening 
variation  during  September? 

12.  What  is  the  ratio  of  the  morning  variation 
during  the  last  week  in  October  to  the  morning 
variation  during  the  first  week  in  September? 

13.  What  is  the  ratio  of  the  evening  variation 
in  the  day's  length  during  October  to  the  evening 
variation  in  September? 

14.  What  is  the  ratio  of  the  evening  variation 
in  the  day's  length  during  the  last  week  of  Octo- 
ber to  the  evening  variation  during  the  first  week 
in  September? 

15.  What  is  the  ratio  of  the  number  of  degrees 
through   which  the   sun  moved  on   the   meridian 
during  October  to  the  number  of  degrees  passed 
through  during  September? 

16.  What  is  the  ratio  of  the  number  of  degrees 
through    which   the  sun   passed  on   the  meridian 
during  October  to  the  entire  number  of  degrees 
passed  through  in  October  and  September? 

17.  The  area  of  the  cross  section  of  the  shadow- 
stick  bears  what   ratio  to  the   area   of  the  shadow 
cast  the  first  week  in  October? 


122  NUMBER  WORK.  [October 

18.  The  area  of  the  shadow  cast  the  first  week  in 
October  bears  what   ratio  to  the  area  cast  the  sec- 
ond week  ?     The  third  ?     The  fourth  ? 

19.  The  area  of  the  shadow  cast  the   first  week 
in  September  bears  what  ratio  to   the  area  of  the 
shadow  cast  the  first  week  in  October? 

20.  The  area   of  the   shadow  cast  the  first  week 
in  September  bears  what   ratio  to  the  area  of  the 
shadow  cast  the  last  week  in  October? 

IV.  PERCENTAGE. 

1.  What  per  cent  of  the  day's  length  was  lost  or 
gained  during  the  first  week  in  October?     During 
the    second?      During    the    third?     During  the 
fourth? 

2.  What  per  cent  of  the  day's  length  at  the  first 
of  the  month  was  gained  or  lost  during  the  entire 
month? 

3.  What  per  cent  of  the  gain  or  loss  in  the  day's 
length     during    the   first    week     occurred   in   the 
morning  ?     During  the  second  ?     During  the  third  ? 
During  the  fourth  ? 

4.  What  per  cent  of  the  gain  or  loss  in  the  day's 
length  during  the  first  week  occurred  in  the  even- 
ing?    During   the    second?      During    the    third? 
During  the  fourth? 

5.  The  gain  or  loss  in  the  day's  length  during 
the  month  in  the  morning  equals  what  per  cent  of 
the  gain  or  loss  during  the  evening? 

6.  The  gain  or  loss  in  the  day's  length  during 
the  first  week  equals  what  per  cent  of  the  gain  or 
loss  during  the  last  week? 

7.  The  movement  of  the  sun  on  the  meridian 


October]  ASTRONOMY.  123 

during  the  first  week  equals  what  per  cent  of  the 
movement  on  the  meridian  for  the  month?  Dur- 
ing the  second  week?  During  the  third  week? 
During  the  fourth  week? 

8.  The  gain  or  loss  in  the  day's  length  during 
October  equals  what  per  cent  of  the  gain  or  loss 
during  September  ? 

9.  The  gain  or  loss  in  the  day's   length   during 
the  last   week  in  October  equals  what  per   cent   of 
the  gain  or  loss  during  the  first  week  in  September? 

10.  The  gain  or  loss  in  the  day's  length  in  the 
morning  during  October  equals  what  per  cent  of 
the  gain  or  loss  in  the  morning  during  September? 

11.  The  gain  or  loss  in  the  day's  length   in   the 
evening  during  October  equals  what  per  cent  of 
the  gain  or  loss  during  the  evening  in  September? 

12.  The  morning  variation  in  the  day's   length 
during  the  last   week  in  October  equals  what  per 
cent  of  the  morning  variation  during  the  first  week 
in  September? 

13.  The  evening  variation  in  the  day's  length 
during  the  last  week  in  October  equals  what  per 
cent  of  the  evening  variation  during  the  first  week 
in  September? 

14.  The   number    of    degrees   on   the    meridian 
through     which   the    sun  passed    during    October 
equals  what  percent  of  the  number  passed  through 
in  September? 

15.  The  number  of    degrees    on   the    meridian 
through  which  the  sun  passed  during  the  last  week 
in  October  equals  what   per   cent  of  the  number 
passed  through  during  the  first  week  in  September? 


124  NUMBER  WORK.  [October 

16.  The    number   of  degrees   on    the   meridian 
through    which   the    sun    passed   during    October 
equals   what  per  cent   of  the   number  of  degrees 
passed  through  during  the  two  months? 

17.  The  area  of  the  cross  section  of  the  shadow- 
stick  equals   what    per  cent    of  the   area    of  the 
shadow  measured  the  first  week  in  October'?     The 
second  ?     The  third  ?     The  fourth  ? 

18.  The  area  of  the   shadow  cast  the  first  week 
in  October  equals  what  per  cent  of  the  area  of  the 
shadow  cast  the  second  week?     The  third?     The 
fourth  ? 

19.  The  area  of  the  shadow  cast  the  first  week 
in  September  equals  what  per  cent  of  the  area  of 
the  shadow  cast  the  first  week  in  October? 

20.  The  area  of  the  shadow  cast  the  first  week 
in  September  equals  what  per  cent  of  the  area  of 
the  shadow  cast  the  last  week  in  October? 


GEOGRAPHY. 


NORTH  AMERICA-DRAINAGE. 

In  the  following  lessons  it  is  designed  to  give  the 
pupils  definite  ideas  respecting  certain  physical 
features  of  North  America  through  a  study  of  its 
great  continental  units,  the  river  basins.  This  is  an 
essential  preliminary  to  an  intelligent  comprehension 
of  the  work  which  will  be  taken  up  later,  referring  to 
the  various  productions,  and  also  to  the  commercial 
relations  of  different  parts  of  the  country. 

I.     WHOLE  NUMBERS. 
A.  River  Basins. 

1.  The   area  of  the   Mississippi  basin    is    how 
much  less  than  the  area  of  the  entire  continent? 

2.  What  is  the  difference  in  area  between  the 
Mississippi   basin    and   the   land  drained  by  the 
rivers  of  the  Atlantic  slope  ? 

3.  What  difference  in  area  between  the  Missis- 
sippi basin  and  the  basin  of  the  St.  Lawrence  ? 

4.  What  difference  in  area  between  the  Missis- 
sippi basin  and  the  basin  of  the  Hudson  Bay  sys- 
tem? 

5.  What  is   the   difference  in  area   between  the 
Mississippi    basin    and  the  basin  of  the  Macken- 
zie? 

125 


126  NUMBER  WORK,  [October 

6.  What  is  the  difference   in  area   between  the 
Mississippi  basin  and  the  basin  of  the  Yukon  ? 

7.  What  is  the  difference  in   area  between  the 
Ohio  basin  and  the  basin  of  the  Missouri? 

8.  What  is  the  difference   in  area  between  the 
Ohio  basin  and  the  slope  drained  by  the  Atlantic 
system  ? 

9.  What  is  the   difference   in   area  between  the 
Ohio  basin  and  the  basin  of  the  St.  Lawrence? 

10.  What  is  the   difference  in  area  between  the 
Ohio  basin  and  the  slope  drained  by  the  Gulf  sys- 
tem? 

11.  What  is  the  difference  in  area  between  the 
Ohio  basin  and  the  basin  of  the  Mackenzie? 

12.  What  is  the  difference  in  area  between  the 
Ohio  basin  and  the  basin  of  the  Yukon? 

13.  What  is  the  difference  in  area  between  the 
Ohio  basin  and  the  basin  of  the  Arkansas? 

14.  What  is  the   difference  in  area  between  the 
Ohio  basin  and  the  basin  of  the  Columbia? 

15.  What  is  the  difference  in  area  between  the 
Ohio  basin  and  the  basin  of  the  Colorado? 

16.  What  is  the  difference  in  area  between  the 
Missouri  basin  and  the  basin  of  the  St.  Lawrence  ? 

17.  What  is  the  difference  in  area  between  the 
Missouri  basin  and  the  basin  of   the   Hudson  Bay 
system  ? 

18.  What  is  the  difference  in  area  between   the 
Missouri  basin  and  the  slope  drained  by  the  Gulf 
system  ? 

19.  What  is  the  difference  in  area   between   the 
Missouri  basin  and  the  basin  of  the  Mackenzie  ? 


October]  GEOGRAPHY  127 

20.  What  is  the  difference  in  area  between  the 
Missouri  basin  and  the  basin  of  the  entire  Missis- 
sippi system? 

21.  What  is  the  difference  in  area  between   the 
St.  Lawrence  basin   and  the  basin  of  the  Hudson 
Bay  system? 

22.  What  is  the  difference   between  the  area   of 
the  St.   Lawrence  basin  and  the  slope   drained  by 
the  Atlantic  system  ? 

B.   Length  of  Rivers- 

23.  What  is  the  difference  in  length  between  the 
Mississippi  Eiver  and  the  Ohio  River?     The  Mis- 
souri ? 

24.  What  is  the  difference  in  length  between  the 
Mississippi  Eiver  smd  the  St.  Lawrence  River? 

25.  What  is  the  difference  in  length  between  the 
Mississippi  River  and  the  Mackenzie  River? 

26.  What  is  the  difference  in  length  between  the 
Mississippi  River  and  the  Columbia  River? 

27.  What  is  the  difference  in  length  between  the 
Mississippi  River  and  the  Yukon  River? 

28.  What  is  the  difference  in  length  between  the 
Missouri  River  and  the  Ohio  River? 

29.  What  is  the  difference  in  length  between  the 
Missouri  River  and  the  St.  Lawrence  River? 

30.  What  is  the  difference  in  length  between  the 
Ohio  River  and  the  St.  Lawrence  River? 

31.  What  is  the  difference  in  length  between  the 
Ohio   River  and  the  Arkansas  River?     The  Red? 

32.  What  is  the  difference  in  length  between  the 
Ohio  River  and  the  Colorado  River?     The  Colum- 
bia? 


128  NUMBER  WORK.  [October 

II.      FllACTIONS. 

A.   River  Basins. 

1.  The    area    of   the    Mississippi    basin    equals 
what  part  of  the  area  of  the  continent  ? 

2.  The  area  of  the  Mississippi  basin  equals  what 
part  of   the  area  drained  by  the  Atlantic  system  ? 

3.  The    area   of   the    Mississippi   basin   equals 
what  part  of  the  area  drained  by  the  St.  Lawrence 
system  ? 

4.  The    area    of   the    Mississippi    basin    equals 
what  part  of  the  area  drained  by  the  Hudson  Bay 
system  ? 

5.  The    area    of   the    Mississippi    basin    equals 
what  part  of  the  area  drained  by  the  Mackenzie 
system  ?  « 

6.  The    area   of   the   Mississippi   basin   equals 
what   part    of    the    area    drained   by    the    Yukon 
system  ? 

7.  The    area    of   the    Mississippi   basin    equals 
what  part  of   the  area  drained  by  the   Columbia 
system?     The  Colorado? 

8.  The  area  of  the   St.  Lawrence  basin   equals 
what   part  of   the  area  drained    by   the    Atlantic 
system  ? 

9.  The  area  of  the  St.  Lawrence  basin  equals 
what  part  of   the  area  drained  by  the  Hudson  Bay 
system  ? 

10.  The  area  of  the  St.  Lawrence  basin  equals 
what  part  of  the  area  drained  by  the  Mackenzie 
system  ? 

11.  The  area  of  the  St.  Lawrence  basin  equals 
what  part  of  the  area  drained  by  the  Gulf  system  ? 


October]  GEOGRAPHY.  129 

12.  The  area  of  the  Ohio  basin  equals  what  part 
of  the  area  drained  by  the  Mississippi  system  ? 

13.  The  area  of  the  Ohio  basin  equals  what  part 
of  the  area  drained  by  the  Missouri  system  ? 

14.  The  area  of  the  Ohio  basin  equals  what  part 
of  the  area  drained  by  the  Atlantic  system  ? 

15.  The  area  of  the  Ohio  basin  equals  what  part 
of  the  area  drained  by  the  Gulf  system? 

16.  The  area  of  the  Ohio  basin  equals  what  part 
of  the  area  drained  by  the  Columbia  system?  The 
Colorado  ?     The  Red  ?     The  Arkansas  ? 

17.  The  area  of  the  Missouri  basin  equals  what 
part  of  the  area  drained  by  the  entire  Mississippi 
system  ? 

18.  The  area  of  the  Missouri  basin  equals  what 
part  of  the  area  drained  by  the  Atlantic  system  ? 

19.  The  area  of  the  Missouri  basin  equals  what 
part  of  the  area  drained  by  the  Gulf  system? 

20.  The  area  of  the  Missouri  basin  equals  what 
part  of  the  area  drained  by  the  Mackenzie  system  ? 

21.  The  area  of  the  Missouri  basin  equals  what 
part  of  the  area  drained  by  the  Yukon  system  ? 

22.  The  area  of  the  Missouri  basin  equals  what 
part  of  the  area  drained  by  the  Columbia  system  ? 

23.  The  area  of  the  Missouri  basin  equals  what 
part  of  the  area  drained  by  the  Colorado  system  ? 

24.  The  area  drained  by  the  Gulf  system  equals 
what   part  of   the    area  drained   by   the   Atlantic 
system  ? 

25.  The  area  drained  by  the  Atlantic   system 
equals  what  part  of  the  area  drained  by  the  Arctic 
system  ? 


130  NUMBER  WORK.  [October 

B.     Length  of  Rivers. 

26.  The  length  of  the  Ohio  River  equals  what 
part  of  the  length  of  the  Mississippi  River. 

27.  The  length  of  the  Ohio  River  equals  what 
part  of  the  length  of  the  Missouri  River. 

28.  The  length  of  the  Ohio  River  equals  what 
part  of  the  length  of  the  St.  Lawrence  River? 

29.  The  length  of  the  St.  Lawrence  River  equals 
what  part  of  the  length  of  the  Mississippi  River? 

30.  The  length  of  the  St.  Lawrence  River  equals 
what  part  of  the  length  of  the  Missouri  River? 

31.  The  length    of   the   St.    Lawrence   River 
equals  what  part  of  the  length  of  the  Mackenzie 
River. 

32.  The  length  of  the  St.  Lawrence  River  equals 
what  part  of  the  length  of  the  Yukon  River? 

33.  The  length  of   the  Missouri  River  equals 
what  part  of  the  length  of  the  Mackenzie  River? 
Of  the  Yukon  River? 

34.  The  length    of   the    Missouri  River  equals 
what  part  of  the  length  of   the  Columbia  River? 
The  Colorado  River? 

III.     RATIO. 

A.   River  Basins. 

1.  What  is  the  ratio  of  the  area  of  the  Missis- 
sippi basin  to  the  area  of  the  entire  continent  ? 

2.  What  is  the  ratio  of  the  area  drained  by  the 
Atlantic  system  to  the  area  of  the  entire  continent  ? 

3.  What  is  the  ratio  of  the  area  drained  by  the 
Gulf  system  to  the  area  of  the  entire  continent  ? 

4.  What  is  the  ratio  of  the  area  of  the  St.  Law- 
rence basin  to  the  area  of  the  Mississippi  basin  ? 


October]  GEOGRAPHY.  131 

5.  What  is  the  ratio  of   the  area  of  the  Atlantic 
slope  to  the   area  of  the  basin  of  the  Mississippi 
River? 

6.  What  is  the  ratio  of  the  area  drained  by  the 
Gulf  system  to  the  area  of  the  Mississippi  basin? 

7.  What   is   the  ratio  of  the  area  of  the  Mac- 
kenzie basin  to  the  area  of  the  Mississippi  basin? 

8.  What  is  the  ratio  of  the  area  of  the  Yukon 
basin  to  the  area  of  the  Mississippi  basin  ? 

9.  What  is  the  ratio  of  the  area  of  the  Colum- 
bia basin  to  the  area  of  the  Mississippi  basin? 

10.  What  is  the  ratio  of  the  area  of  the  Colorado 
basin  to  the  area  of  the  Mississippi  basin  ? 

11.  What  is  the  ratio  of  the  area  of  the  Ohio 
basin  to  the  area  of  the  Mississippi  basin  ? 

12.  What  is  the  ratio  of  the  area  of  the  Mis- 
souri basin  to  the  area  of  the  Mississippi  basin? 

13.  What  is  the  ratio  of  the  area  of  the  Ohio 
basin  to  the  area  of  the  Missouri  basin  ? 

14.  What  is  the  ratio  of  the  area  of  the   Ohio 
basin  to  the  area  of  the  St.  Lawrence  basin. 

15.  What  is  the  ratio  of  the  area  of  the  Ohio 
basin  to  the  area  drained  by  the  Atlantic  system? 

16.  What  is  the  ratio  of  the   area  of  the  Ohio 
basin  to  the  area  drained  by  the  Gulf  system  ? 

17.  What  is  the   ratio  of  the  area  of  the  Ohio 
basin  to  the  area  of  the  Mackenzie  basin? 

18.  What  is  the  ratio  of  the  area  of  the  Ohio 
basin  to  the  area  of  the  Yukon  basin  ? 

19.  What  is  the  ratio  of  the  area  of  the  Ohio 
basin  to  the  area  of  the  Columbia  basin  ? 

20.  What  is  the  ratio  of  the  area  of  the  Ohio 
basin  to  the  area  of  the  Colorado  basin  ? 


132  NUMBER  WORK.  [October 

21.  What  is  the  ratio  of  the  area  of  the  Ohio 
basin  to  the  area  of  the  Arkansas  basin? 

22.  What  is  the  ratio  of  the  area   of  the  Ohio 
basin  to  the  area  of  the  Red  River  basin  ? 

23.  What  is  the  ratio  of  the  area  of  the  St.  Law- 
rence basin  to  the  area  of  the  Mackenzie  basin? 

24.  What  is  the  ratio  of  the  area  of  the  St.  Law- 
rence basin  to  the  area   drained   by  the   Atlantic 
system  ? 

25.  What  is  the  ratio  of  the  area  of  the  St.  Law- 
rence basin  to  the  area  of  the   Columbia  basin? 
The  Colorado  basin? 

JE>.   Length  of  Rivers. 

26.  The  length   of  the  Ohio  River  bears  what 
ratio  to  the  length  of  the  Mississippi  River? 

27.  The  length  of  the  Ohio  River  bears  what 
ratio  to  the  length  of  the  Missouri  River? 

28.  The  length  of  the   Ohio  River  bears  what 
ratio  to  the  length  of  the  St.  Lawrence  River? 

29.  The  length  of  the  Ohio  bears  what  ratio  to 
the  length  of  the  Columbia  River  ?     The  Colorado 
River?     The  Arkansas  River?     The  Red.  River? 

30.  The  length  of  the  St.  Lawrence  River  bears 
what  ratio  to  the  length  of  the  Mississippi  River? 

31.  The  length   of  the   Mackenzie  River  bears 
what  ratio  to  the  length  of  the  Mississippi  River? 

32.  The  length  of  the  Yukon  River  bears  what 
ratio  to  the  length  of  the  Mississippi  River? 

33.  The  length   of  the   Columbia   River  bears 
what  ratio  to  the  length   of  the  Colorado  River? 
The  Arkansas  River?     The  Red  River? 

34.  The    length    of    navigable    waters    in     the 


October]  GEOGRATIIY.  133 

Mississippi   system   bears  what  ratio  to   the  total 
length  of  the  rivers  in  this  system  ? 
IV.     PERCENTAGE. 
A.     fiiver  Basins. 

1.  The  area  of  the  Mississippi  basin  equals  what 
per  cent  of  the  area  of  the  continent? 

2.  The   area   drained    by    the   Atlantic   system 
equals  what  per  cent  of  the  area  of  the  continent? 

3.  The  area  drained  by  the  Gulf  system  equals 
what  per  cent  of  the  area  of  the  continent  ? 

4.  The  area  of  the  Ohio  basin  equals  what  per 
cent  of  the  area  of  the  Mississippi  basin? 

5.  The  area  of  the  Missouri  basin   equals  what 
per  cent  of  the  area  of  the  Mississippi  basin  ? 

6.  The  area  of-  the  Arkansas  basin  equals  what 
per  cent  of  the  area  of  the  Mississippi  basin  ? 

7.  The  area  of  the  Ked  River  basin  equals  what 
per  cent  of  the  area  of  the  Mississippi  basin  ? 

8.  The  area  of  the  St.  Lawrence  basin  equals 
what  per  cent  of    the    area    of    the    Mississippi 
basin  ? 

9.  The    area  drained    by    the    Atlantic  system 
equals  what  per  cent  of  the  area  of  the  Mississippi 
basin  ? 

10.  The  area  drained  by  the  Gulf  system  equals 
what    per    cent    of    the    area    of    the  Mississippi 
basin  ? 

11.  The    area  of    the  Mackenzie    basin   equals 
what    per    cent    of    the    area  of    the  Mississippi 
basin  ? 

12.  The  area  of  the  Yukon   basin   equals   what 
[XT  cent  of  the  area  of  the  Mississippi  basin? 


134  NUMBER  WORK.  [October 

13.  The  area  of  the  Columbia  basin  equals  what 
percent  of  the  area  of  the  Mississippi  basin? 

14.  The  area  of  the  Colorado  basin  equals  what 
per  cent  of  the  area  of  the  Mississippi  basin  ? 

15.  The  area  of  the  Ohio  basin  equals  what  per 
cent  of  the  area  of  the  St.  Lawrence  basin  ? 

16.  The  area  of  the  Ohio  basin  equals  what  per 
cent  of  the  area  drained  by  the  Atlantic  system? 

17.  The  area  of  the  Ohio  basin  equals  what  per 
cent  of  the  area  drained  by  the  Gulf  system? 

18.  The  area  of  the  Ohio  basin  equals  what  per 
cent  of  the  area  of  the  Missouri  basin  ? 

19.  The  area  of  the  Ohio  basin  equals  what  per 
cent  of  the  area  of  the  Columbia  basin? 

20.  The  area  of  the  Ohio  basin  equals  what  per 
cent  of  the  area  of  the  Colorado  basin? 

21.  The  area  of  the  Ohio  basin  equals  what  per 
cent  of  the  area  of  the  Arkansas  basin  ?     The  Red 
River  basin  ? 

22.  The  area  of  the   Missouri  basin  equals  what 
per  cent  of  the  area  of  the  St.  Lawrence  basin  ? 

23.  The  area  of  the  Missouri  basin  equals  what 
per  cent  of  the  area  drained  by   the  Atlantic  sys- 
tem. 

24.  The  area  of  the  Missouri  basin  equals  what 
per  cent  of  the  area  of  the  Mackenzie  basin  ? 

25.  The  area  of  the  Missouri  basin  equals  what 
per  cent  of  the  area  of  the  Columbia  basin  ?     The 
Colorado  basin? 

B.    Length  of  Rivers. 

26.  The  length  of   the  Ohio  River  equals   what 
per  cent  of  the  length  of  the  Mississippi  River  ? 


October]  GEOGRAPHY.  135 

27.  The  length  of  the  Missouri  River  equals  what 
IHT  cent  of  the  length  of  the  Mississippi  River? 

28.  The  length  of  the  Arkansas  equals  what  per 
c-ent  of  the  length  of  the  Mississippi  River? 

29.  The  length    of  the  Red  River  equals   what 
pi-r  cent  of  the  length  of  the  Mississippi  River? 

30.  The   length    of    the  St.    Lawrence    River 
equals  what  per  cent  of  the  length  of  the  Missis- 
sippi River? 

31.  The  length  of  the  Mackenzie   River  equals 
what   per  cent  of  the   length   of   the    Mississippi 
River? 

32.  The  length  of  the  Yukon  River  equals  what 
per  cent  of  the  length  of  the  Mississippi  River? 

33.  The  length  of   the  Columbia  River  equals 
what  per  cent  of  the    length   of  the  Mississippi 
River? 

34.  The  length   of  the  Colorado  River  equals 
what  per  cent  of   the    length  of   the  Mississippi 
River? 

35.  The  length  of  the  Ohio  River  equals  what 
per  cent  of  the  length  of  the  St.  Lawrence  River? 

36.  The  length  of  the  Ohio  River  equals  what 
per  cent  of  the  length  of  the  Missouri  River? 

37.  The  length  of  the  Ohio  River  equals  what 
per  cent  of  the  length  of  the  Columbia  River? 

38.  The  length  of  the  Ohio  River  equals  what 
per  cent  of  the  length  of  the  Colorado  River? 

39.  The  length  of  the  Missouri  River  equals  what 
per  cent  of  the  length  of  the  St.  Lawrence  River? 

40.  The  length  of  the  Missouri  River  equals  what 
per  cent  of  the  length  of  the  Mackenzie  River? 


MINERALOGY. 


PHYSICAL  PROPERTIES  OF  MINERALS. 

The  following  problems  may  be  used  in  different 
ways,  varying  with  the  method  of  study  pursued. 
They  may  be  used  in  reviewing  the  work  previously 
done,  or  they  may  be  used  after  a  field  lesson  in 
giving  the  pupils  a  more  definite  idea  of  the  pro- 
portions in  which  the  different  minerals  are  to  be 
found  in  the  neighborhood.  The  class  may  be 
required  to  group  their  entire  collection  with  respect 
to  luster,  for  example,  and  then  note  the  number  in 
each  group  and  the  comparative  size  of  the  different 
groups.  In  this  way,  the  physical  properties  may 
be  taught  or  reviewed  and  a  knowledge  of  the  rela- 
tive numbers  may  be  gained  at  the  same  time. 

PROBLEMS. 
I.     WHOLE  NUMBERS. 

1.  How  many  minerals  have  you  in  your  entire 
collection  ? 

2.  How  many  minerals   have  you  with  metallic 
luster  ? 

3.  How   many    minerals    have    you   with    non- 
metallic  luster? 

4.  How  many  minerals  have  you  with  glassy  or 
vitreous  luster?     Pearly  luster?    Resinous  luster? 

136 


October]  MINERALOGY.  137 

Pitchy    luster?     Silky   luster?     Greasy   or   waxy 
luster?     Dull  luster? 

5.  How  many  minerals  have  you  that  are  trans- 
parent?    Opaque?    Translucent?    Semi-transpar- 
ent ?     Sub-translucent  ? 

6.  How  many  minerals  have  you  that  are  very 
hard,  i.  e.,  scratch  glass  or  quartz  ? 

7.  How  many  minerals  have  you  that  are  hard, 
i.  e.,not  easily  scratched  by  a  knife — scratch  glass. 

8.  How  many  minerals  have  you  that  are  soft, 
i.  e.,  can  not  be  scratched  with  finger  nail — easily 
scratched  with  a  knife? 

9.  How  many   minerals  have  you  that  are  very 
soft,  i.  e.,  can  be  scratched  with  the  finger  nail  or 
very  easily  with  a  knife? 

10.  How    many  of   your    minerals  are  brittle? 
Malleable?     Sectile?     Flexible?     Elastic? 

11.  How    many   of  your   minerals    dissolve  «in 
acid?     How  many  are  insoluble  in  acid? 

12.  How  many  of  your  minerals  are  fusible? 
How  many  are  infusible? 

13.  How  many  of  your  minerals  have  a  white 
streak?      Black  streak?      Brown    streak?      Red 
streak?     Yellow  streak? 

14.  How  many  minerals  have  you  whose  streak 
is  the  same  color  as  that  of  the  mineral?     How 
many  different? 

15.  How    many    minerals    have    you    that    are 
crystalline?     How  many  are  not  so? 

16.  Which  is  greater,  and  how  much,  the  num- 
ber with  metallic,  or  the  number  with  non-metallic 
luster? 


138  NUMBER  WORK.  [October 

17.  Which  is  greater,  and  how  much,  the  num- 
ber   of    transparent,    or   the   number    of   opaque 
minerals  ? 

18.  Which  is  greater,  and  how  much,  the  num- 
ber of  transparent,  or  the  number  of  translucent 
minerals  ? 

19.  Which  is  greater,  and  how  much,  the   num- 
ber of  minerals  that  are  very  hard,  or  the  number 
that  are  very  soft? 

20.  Which  is  greater,  and  how  much,  the  num- 
ber of  minerals   soluble    in  acid,    or  the  number 
insoluble? 

21.  Which  is  greater,  and  how  much,  the  num- 
ber of  minerals   fusible  or  the  number  infusible? 

22.  Which  is  greater,  and  how  much,  the  num- 
ber of  crystalline,  or  the  number  of  non-crystalline 
minerals  ? 

II.     FRACTIONS. 

1.  What    part  of  your  collection    has    metallic 
luster?     Non-metallic? 

2.  What    part  of   your    collection    has  vitreous 
luster?      Pearly?      Eesinous?      Pitchy?      Silky? 
Waxy  or  greasy  ?     Dull  ? 

3.  What  part  of  your  collection  is  transparent? 
Translucent?  Semi-transparent?  Sub-translucent? 
Opaque? 

4.  What  part  of   your  collection  is  very  hard, 
i.  e.y  will  scratch  glass  or  quartz? 

5.  What  part  of    your  collection  is  hard,  i.  e., 
not  easily  scratched  by  a  knife — will  scratch  glass  ? 

6.  What  part  of  your  collection  is  soft,  i.  e.,  can 


October]  MINERALOGY.  139 

not    be    scratched   with    the    linger   nail  —  easily 
scratched  by  a  knife? 

7.  What  part  of  your  collection  is  very  soft,  i.  c., 
can    be    scratched    by    finger   nail  —  very  easily 
scratched  by  a  knife? 

8.  What    part    of     your   collection    is    brittle? 
Malleable?     Sectile?     Flexible?     Elastic? 

9.  What  part  of    your  collection  is  soluble   in 
acid?     What  part  is  insoluble? 

10.  What  part  of  your  collection  is  fusible? 

11.  What  part  of  your  collection  is  infusible? 

12.  What  part  of  your  collection  has  a  white 
streak?     Black    streak?      Brown    streak?      Red 
streak?     Yellow  streak? 

13.  What  part  of  your  minerals  has   streak  and 
color  alike?     What  part  unlike? 

14.  What  part  of  your  collection  is  crystalline? 
What  part  is  not  so? 

15.  What    part   of   your    minerals  is  foliated? 
Stratified?     Amorphous? 

16.  The    minerals    with    metallic    luster    equal 
what  part  of  the  number  non-metallic  ? 

17.  The    minerals   that    are    transparent   equal 
what  part  of  the  number  that  are  opaque  ? 

18.  The  number  of  minerals  that  are  very  hard 
equals  what  part  of  the  number  that  are  very  soft? 

19.  The  number  of  minerals  that  are  soluble  in 
acid   equals    what  part    of  the    number  that    are 
insoluble? 

20.  The  number  of   minerals  that  are    fusible 
equals  what  part   of   the   number  that  are   infusi- 
ble? 


140  NUMBER  WORK.  [October 

21.  The   number   of    amorphous    forms  equals 
what  part  of  the  number  of  crystalline  forms? 
III.  RATIO. 

1.  What  is  the  ratio  of  the  number  of  minerals 
with  metallic  luster  to  the  number  in  the  entire 
collection?     Of  the  non-metallic? 

2.  What  is  the  ratio  of  the  number  of  minerals 
with  vitreous  luster  to  the  number  in  your  entire 
collection?     Of   the  number   with  pearly  luster? 
Of   the  number  with    resinous   luster?      Of   the 
number  with  pitchy  luster?     Of  the  number  with 
silky  luster?     Of   the  number  with  waxy  luster? 
Of  the  number  with  dull  luster? 

3.  What  is  the  ratio  of  the  number  of  minerals 
that  are  transparent  to  the  number  in  your  entire 
collection?     Of  the  number  that  are   semi-trans- 
parent?    Of  the  number  that  are  translucent?  Of 
the  number  that    are   sub-translucent?      Of    the 
number  that  are  opaque? 

4.  What  is  the  ratio  of  the  number  of  minerals 
that  are  very  hard  (see  previous   lessons)  to  the 
number  in  your  entire  collection?    Of  the  number 
that    are  hard?     Of  the  number  that   are    soft? 
Of  the  number  that  are  very  soft? 

5.  What  is  the  ratio  of  the  number  of  minerals 
in  your  collection  that  are  brittle   to  your  entire 
number?     Of    the    number    that    are    malleable? 
Of  the  number  that  are  sectile?     Of  the  number 
that  are  flexible?    Of  the  number  that  are  elastic? 

6.  What  is  the  ratio  of  the  number  of  minerals 
that   are  soluble  in   acid  to  the  number  in  your 
entire  collection  ?  Of  the  number  that  are  insoluble  ? 


October]  MINERALOCY.  141 

7.  What  is  the  ratio  of   the  number  of  minerals 
that    are    fusible   to    the    number   in   your   entire 
collection  ?     Of  the  number  that  are  infusible  ? 

8.  What  is  the  ratio  of  the  number  of  minerals 
with  a  white  streak  to  the  number  in  your  entire 
collection  ?    Of  the  number  with  black  streak  ?    Of 
the  number  with  brown  streak?     Of  the  number 
with   red    streak?     Of    the    number    with    yellow 
streak  ? 

9.  What  is  the  ratio  of  the  number  of  minerals 
which   have  streak  and  color   alike   to  the   whole 
number  in  your  entire  collection?     Of    those  with 
streak  and  color  different? 

10.  What  is  the  ratio  of  the  number  of   crys- 
talline forms  in  your  collection  to  the  whole  num- 
ber? 

11.  Wliat  is  the  ratio  of  the  number  of  trans- 
parent minerals  to  the  number  of  opaque  minerals? 

12.  What  is  the  ratio  of    the   number  of  very 
hard  minerals  to  the  number  of  very  soft? 

13.  What  is  the  ratio  of  the  number  of  minerals 
soluble  in  acid  to  the  number  insoluble? 

14.  What  is  the  ratio  of  the  number  of  minerals 
that  are  fusible  to  the  number  infusible? 

15.  What   is  the  ratio  of  the  number  of  crys- 
talline minerals  to  the  number  non-crystalline? 

IV.  PERCENTAGE. 

1.  What  per  cent  of  your  minerals  have  metallic 
luster? 

2.  What   per  cent   of  your  minerals  have   non- 
metallic  luster? 

3.  What    per    cent    of     your    minerals    have 


142  NUMBER  WORK.  [October 

vitreous    luster?      Pearly?      Resinous?      Pitchy? 
Silky?     Waxy  or  greasy?     Dull? 

4.  What  per  cent  of  your  minerals  are  very  hard? 
(See  previous  lessons  for  scale  of  hardness.) 

5.  What  per  cent  of  your  minerals  are  hard? 

6.  What  per  cent  of  your  minerals  are  soft? 

7.  What  per  cent  of  your  minerals  are  very  soft? 

8.  What  per  cent  of  your  minerals  are  brittle? 
Malleable?     Sectile?     Flexible?     Elastic? 

9.  What  per  cent  of  your  minerals  are  soluble 
in  acid? 

10.  What  per  cent  of  your  minerals  are  insolu- 
ble in  acid? 

11.  What  per  cent  of  your  minerals  are  fusible? 

12.  What  per  cent  of  your  minerals  are  infusi- 
ble? 

13.  What  percent  of  your  minerals  have  a  white 
streak?  Black  streak?  Brown  streak?  Red  streak? 
Yellow  streak? 

14.  What  per  cent  of  your  minerals  have  color 
and  streak  alike? 

15.  What  per  cent  of  your  minerals  have  color 
and  streak  different  ? 

16.  What  per  cent   of  your  minerals  are  crys- 
talline?    Amorphous?     Foliated?     Fibrous? 

17.  The  minerals  with  metallic  luster  equal  what 
per  cent  of  the  minerals  that  are  non-metallic  ? 

18.  The  transparent   minerals   equal   what  per 
cent  of  the  opaque  minerals? 

19.  The  transparent  minerals   equal   what   pel- 
cent  of  the  translucent  minerals  ? 


October]  MINERALOGY.  143 

20.  The  very  hard  minerals  equal  what  per  cent 
of  the  very  soft  minerals? 

21.  The  minerals  soluble  in  acid  equal  what  per 
cent  of  the  minerals  that  are  insoluble? 

22.  The  fusible  minerals  equal  what  per  cent  of 
the  minerals  that  are  infusible? 

23.  The  amorphous  forms  equal  what  per  cent 
of  the  minerals  that  are  crystalline  V 


ZOOLOGY. 


WINTER  HABITS  OF  ANIMALS. 

The  pupils  should  make  a  complete  list  of  all  the 
animals  that  inhabit  the  surrounding  country  during 
the  whole  or  any  part  of  the  year.  The  present  con- 
dition of  these  should  be  studied,  and  the  groups 
given  below  are  suggested  for  the  purpose  of  giving 
more  definite  ideas  concerning  this  interesting  period 
of  animal  life.  From  the  swift-winged  bird  at 
one  extreme,  through  almost  every  possible  interme- 
diate gradation,  to  the  reptile  in  a  state  of  complete 
stupefaction  at  the  other,  one  sees  a  plasticity  of  the 
animal  organism  that  is  truly  remarkable;  and,  when 
it  is  remembered  that  the  same  laws  of  nutrition, 
assimilation,  and  excretion  govern  all,  nothing  more 
clearly  than  this  study  shows  the  extreme  modifica- 
tions'which  the  animal  functions  and  structure  may 
undergo  without  destroying  the  organism  itself.  The 
animals  with  which  the  pupils  are  familiar  may  be 
grouped  as  follows: 

1.  Animals    that    migrate    on    the    approach    of 
winter. 

2.  Animals  that  remain  and  feed  abroad  during 
the  winter. 

3.  Animals  that  store  food  for  winter  use. 

4.  Animals  that  hibernate  without  food. 

144 


November]  ZOOLOGY.  145 

5.  Animals  that  die  on  the  approach  of  winter. 

6.  Animals  that  appear  in  the  neighborhood  dur- 
ing winter  only. 

PROBLEMS. 
I.     WHOLE  NUMBERS. 

1.  How  many  different  kinds  of  animals  migrate 
in  autumn? 

2.  How  many  different  kinds  of  animals  remain 
abroad  to  feed  during  the  winter? 

3.  How  many  different  kinds  of  animals  store 
food  for  winter  use? 

4.  How  many  different  kinds  of   animals  hiber- 
nate without  food? 

5.  How  many  different  kinds  of  animals  die  on 
the  approach  of  winter? 

6.  How  many  different  kinds  of   animals  appear 
only  in  winter? 

7.  How  many  different  kinds  of  animals  remain 
in  the  neighborhood,  in  one  condition  or  another, 
during  the  entire  winter? 

8.  Which  is  greater,  and  how  much,  the  number 
of  animals  migrating  or  the  number  staying? 

9.  Which  is  greater,  and  how  much,  the  number 
of  different  kinds  of  animals  that  store  food   for 
winter  or  the  number  that  hibernate  without  it? 

10.  Which  is  greater,  and  how  much,  the  num- 
ber of  different  kinds  of  animals  that  die,  or  the 
number  that  live  through  the  winter? 

11.  Which  is  greater,  and  how  much,  the  num- 
ber of   different  kinds  of  animals  that   hibernate 
without  food  or   the  number  which   feed  abroad 
during  winter? 


140  NUMBER  WORK.  [November 

12.  Which  is  greater,  and  how  much,  the  num- 
ber of  different  kinds  of  animals  which  appear 
only  in  winter  or  the  number  which  migrate  ? 

II.     FRACTIONS. 

1.  The   number   of    different  kinds   of  animals 
that  migrate  equals  what  part  of  all  the  different 
kinds  of  animals  in  the  neighborhood  ? 

2.  The  number  of    different  kinds   of  animals 
that  remain  and   feed   abroad   during   the   winter 
equals  what  part  of  the  whole   number  belonging 
to  the  region  ? 

3.  The  number  of  different   kinds  of    animals 
that  store  food  equals  what  part  of  the  whole  num- 
ber of  different  kinds? 

4.  The  number  of    different   kinds    of  animals 
that  hibernate   without  food  equals  what   part  of 
the  whole  number  ? 

5.  The  number  of    different  kinds   of   animals 
that  die  on  the  approach  of  winter    equals  what 
part  of  the  whole  number? 

6.  The  number  of    different   kinds   of  animals 
that  appear  only  during  winter  equals  what  part  of 
the  whole  number? 

7.  The  number  of    different   kinds   of   animals 
migrating  equals  what  part  of  the  number  of  dif- 
ferent kinds  which  remain  abroad  ? 

8.  The  number  of  different  kinds    of    animals 
storing  food  equals   what   part   of  the  number  of 
different   kinds    which    feed    abroad?       Of   those 
which  migrate? 

9.  The  number  of  different   kinds    of   animals 


November]  ZOOLOGY.  147 

hibernating  equals   what   part  of  the   number   of 
different  kinds  which  store  food? 

10.  The  number  of  different  kinds   of  animals 
hibernating  equals   what  part   of    the  number  of 
different  kinds  which  feed  abroad  ? 

11.  The  number  of  different   kinds  of  animals 
that  die  on  the   approach  of  winter  equals  what 
part  of  the  number  of  different  kinds  which  hiber- 
nate? 

12.  The  number  of  different  kinds  of  animals 
that  die  on  the   approach  of  winter  equals  what 
part  of  the  number  of  different  kinds  which  store 
food? 

»   13.  The  number  of  different  kinds   of  animals 
that  die  on  the  approach  of  winter  equals  what  part 
of  the  number  of  different  kinds  which  feed  abroad  ? 
14.  The   number  of  different  kinds  of  animals 
that  appear  only  in  winter  equals  what  part  of  the 
number  of  different  kinds  that  migrate? 
III.     RATIO. 

1.  What  is  the  ratio  of  the  number  of  different 
kinds  of  animals  that  migrate  to  the  entire  num- 
ber of  different  kinds  in  the  region? 

2.  What  is  the  ratio  of  the  number  of  different 
kinds  of  animals  that   feed  abroad  to  the  entire 
number  of  different  kinds  belonging  to  the  region? 

3.  What  is  the  ratio  of  the  number  of  different 
kinds  of  animals  that  store  food  to  the  entire  num- 
ber of  different  kinds  belonging  to  the  region  ? 

4.  What  is  the  ratio  of  the  number  of  different 
kinds  of  animals  that  hibernate  to  the  entire  num- 
ber belonging  to  the  region  ? 


148  NUMBER  WORK.  [November 

5.  What  is  the  ratio  of  the  number  of  different 
kinds   of    animals   that   die    on    the    approach  of 
winter   to  the  entire  number  of    different   kinds 
belonging  to  the  region  ? 

6.  What  is  the  ratio  of  the  number  of  different 
kinds   of   animals   that    appear   only   during   the 
winter   to   the    entire   number  of  different    kinds 
belonging  to  the  region  ? 

7.  What  is  the  ratio  of  the  number  of  different 
kinds   of    animals    that    feed   abroad    during   the 
winter   to    the    number   of    different    kinds   that 
migrate  ? 

8.  What  is  the  ratio  of  the  number  of  different 
kinds    of    animals    that   feed   abroad   during   the 
winter  to  the  number  of  different  kinds  that  store 
food? 

9.  What  is  the  ratio  of   the  number  of  different 
kinds  of  animals  that  feed  abroad  during  the  winter 
to  the  number  of  different  kinds  that  hibernate? 

10.  What  is  the  ratio  of  the  number  of  different 
kinds   of    animals    that   feed   abroad    during  the 
winter  to  the  number  of  different   kinds  that  die 
on  the  approach  of  winter? 

11.  What  is  the  ratio  of  the  number  of  different 
kinds  of  animals  that  store  food  to  the  number  of 
different  kinds  that  hibernate? 

12.  What  is  the  ratio  of  the  number  of  different 
kinds  of  animals  that  store  food  to  the  number  of 
different  kinds  that  die  on  the  approach  of  winter? 

13.  What  is  the  ratio  of  the  number  of  different 
kinds  of  animals  that  hibernate  to  the  number  of 
different  kinds  that  die  on  the  approach  of  winter? 


November]  ZOOLOGY.  U9 

14.  What  is  the  ratio  of  the  number  of  different 
kinds  of  animals  that  hibernate  to  the  number  of 
different  kinds  that  appear  only  in  winter? 

IV.     PERCENTAGE. 

1.  What    per   cent    of    the    different    kinds   of 
animals  that  belong  to  the  region  migrate? 

2.  What    per   cent    of    the    different    kinds    of 
animals  that  belong  to  the  region  feed  abroad  dur- 
ing the  winter? 

3.  What   per   cent    of    the    different    kinds   of 
animals  that  belong  to  the  region  store  food  for 
the  winter? 

4.  What    per   cent    of    the   different    kinds    of 
animals  that  belong  to  the  region  hibernate  without 
food? 

5.  What    per   cent    of    the   different    kinds   of 
animals  that    belong  to   the    region  die    on   the 
approach  of  winter? 

6.  What    per   cent   of    the   different    kinds    of 
animals   that   belong   to   the    region  appear    only 
during  winter? 

7.  The  different  kinds  of  animals   that   migrate 
equal  what  per  cent  of  the  different  kinds  that  feed 
abroad  during  the  winter? 

8.  The  different  kinds  of  animals  that  migrate 

O 

equal  what  per  cent  of  the  different  kinds  that 
store  food  for  winter? 

9  The  different,  kinds  of  animals  that  migrate 
equal  what  per  cent  of  the  different  kinds  that 
hibernate? 

10.  The  different  kinds  of  animals  that  migrate 


150  NUMBER  WORK.  [November 

equal  what  per  cent  of  the  different  kinds  that  die 
on  the  approach  of  winter  ? 

11.  The  different  kinds    of    animals   that  feed 
abroad  during  the  winter  equal  what  per  cent  of 
the  different  kinds  that  store  food  for  the  winter? 

12.  The   different   kinds  of   animals   that   feed 
abroad  during  the  winter  equal  what  per  cent  of 
the  different  kinds  that  hibernate  ? 

13.  The    different   kinds  of   animals    that    feed 
abroad  during  the  winter  equal  what  per  cent  of 
the  different  kinds  that  die  on  approach  of  winter? 

14.  The  different    kinds  of  animals  that   store 
food  for  winter  equal  what  per  cent  of  the  different 
kinds  that  hibernate? 

15.  The    different    kinds  of  animals  that  store 
food  for  winter  equal  what  per  cent  of  the  different 
kinds  that  die  on  approach  of  winter? 

16.  The  different  kinds  of  animals  that  hiber- 
nate  without    food  equal    what    per  cent    of   the 
different  kinds  that  die  on  approach  of  winter? 

17.  The  different  kinds  of  animals  that  die  on 
the  approach  of  winter  equal  what  per  cent  of  the 
different  kinds  that  appear  only  during  the  winter? 


BOTANY. 


ANNUALS,  BIENNIALS,  AND   PERENNIALS. 

The  lessons  under  this  head  are  designed  to  give 
the  pupils  somewhat  definite  ideas  of  how  plants 
prepare  themselves  for  the  winter  season.  Com- 
paratively few  plants  carry  their  leaves  through  this 
season;  a  larger  number  have  their  hopes  for  the 
future  stored  up  in  a  multitude  of  buds;  others 
depend  upon  materials  stored  in  roots  or  stems, 
while  a  great  host  depends  upon  the  seeds  only. 
The  following  classes  may,  therefore,  be  consid- 
ered : 

1.  Those  with  leaves  the  year  round — evergreens 
—perennials. 

2.  Those  growing  from  year  to  year — the  living 
material  being  found    during  the  winter  chiefly   in 
buds — perennials. 

3.  Those  preparing  a  root  or  stalk  for  the  second 
season  only — biennials. 

4.  Those  dying,  root  and  branch,  the  seed  only 
being  preserved — annuals. 

PROBLEMS. 
I.     WHOLE  NUMBERS. 

1.  How  many  different  kinds  of  trees  or  plants 
can  you  find  that  bear  leaves  the  year  round  ? 
151 


152  NUMBER  WORK.  [November 

2.  How    many    different    kinds    of    plants    live 
through  the  winter  but  lose  their  leaves? 

3.  How  many  different  kinds  of  plants  can  you 
find    that  die  down   to  the  root  in  the  fall — the 
latter  being  preserved  alive  during  the  winter? 

4.  How  many  different  kinds  of   plants  can  you 
find  that  die,  root-  and  stem,  at    the  approach  of 
winter? 

5.  Which  is  the  larger,  and  how  much,  the  num- 
ber of  different  kinds  of  plants  that  live  through 
the  winter  or  the  number  of  different  kinds  that 
die  in  autumn? 

6.  How  many  different  kinds  of  plants  can  you 
find  tjiat  produce  both  seeds  and  buds  ? 

7.  How  many  different  kinds  of  plants  can  you 
find    that   begin    winter   without    having    formed 
seeds  ? 

8.  How  many  different  kinds  of  perennials  can 
you  find? 

9.  How  many  different  kinds  of  biennials  can 
you  find? 

10.  How  many  different   kinds   of  annuals  can 
you  find? 

11.  Which  is  larger,  and  how  much,  the  num- 
ber of  different  kinds  of  perennials  or  ths  number 
of  different  kinds  of  biennials? 

12.  Which  is  larger,  and  how  much,  the  num- 
ber of  different  kinds  of  perennials  or  the  number 
of  different  kinds  of  annuals? 

II.     FRACTIONS. 

1.  What  part  of  all  the  different  kinds  of  plants 
that  you  can  find  bears  leaves  the  year  round? 


November]  BOTANY.  133 

2.  What  part  of   the  entire  number  of  different 
kinds  of  plants  observed  loses  its  leaves  in  autumn? 

3.  What  part  of  the  entire  number  of   different 
kinds  of  plants  dies  down  to  the  root  in  autumn  ? 

4.  What  part  of  the  entire  number  of   different 
kinds  of  plants  dies,  root  and  stem,  in  autumn? 

5.  What  part  of  the  entire  number  of   different 
kinds  of  plants  lives  through  the  winter? 

6.  What  part  of  the  entire  number  of  different 
kinds  of  plants  produces  both  seeds  and  buds? 

7.  What  part  of  the  entire  number  of  different 
kinds   of    plants    begins    winter    without    having 
formed  seeds? 

8.  The  perennials  equal  what  part  of   all  the 
different  kinds  of  plants  you  can  find? 

9.  The  biennials  equal  what  part  of  the  entire 
number  of  different  kinds  of   plants  that  you  can 
find? 

10.  The  annuals  equal  what  part  of  the  whole 
number  of  different  kinds   of  plants  that  you  can 
find? 

11.  The  number  of  biennials  equals  what  part 
of  the  number  of  perennials  ? 

12.  The  number  of  annuals  equals  what  part  of 
the  number"  of  perennials  ? 

III.     RATIO. 

1.  The  number  of  different  kinds  of  plants  that 
bear  leaves  the  year  round  bears  what  ratio  to  the 
entire  number  of  different  kinds  that  you  can  find? 

2.  What  is  the  ratio  of   the  different  kinds  of 
plants   that    lose   their  leaves    in    autumn    to  the 
entire  number  of  different  kinds? 


154  NUMBER  WORK.  [November 

3.  What  is   the  ratio  of  the  different  kinds  of 
plants  that  die  down  to  the  root  in  autumn  to  the 
entire  number  of  different  kinds  ? 

4.  What  is  the  ratio  of  the  different  kinds  of 
plants  that  die,  root  and  branch,  in  autumn  to  the 
entire  number  of  different  kinds? 

5.  What  is  the  ratio  of  the  number  of  different 
kinds  of   plants  that  live   through  the  winter  to 
the  whole  number  of  different  kinds? 

6.  What  is  the  ratio  of  the  number  of  different 
kinds  of  plants  that  produce  both  seeds  and, buds 
to  the  entire  number  of  different  kinds  ? 

7.  What  is  the  ratio  of  the  different  kinds  of 
plants  that  begin  winter  without  having  matured 
seeds  to  the  entire  number  of  different  kinds? 

8.  What  is  the  ratio  of   the  evergreens  to  the 
entire  number  of  perennials  ? 

9.  What  is  the  ratio  of  the   perennials  to  the 
whole  number  of  different  kinds  of  plants  ? 

10.  What  is  the  ratio  of  the  biennials  to  the 
whole  number  of  different  kinds  of  plants? 

11.  What    is   the    ratio    of  the  annuals  to   the 
whole  number  of  different  kinds  of  plants? 

12.  What    is    the  ratio  of    the   annuals   to  the 
perennials  ? 

13.  What  is  the   ratio  of  the   annuals  to  the 
biennials  ? 

14.  What  is  the  ratio  of   the  biennials  to  the 
perennials  ? 

IV.     PERCENTAGE. 

1.  What  per  cent  of  all  the  different  kinds  of 
plants  that  you  can  find  bear  leaves  the  year  round? 


November]  BOTANY.  155 

2.  What  per  cent  of  the  different  kinds  of  plants 
that  you  have  observed  lose  their  leaves  in  autumn  ? 

;}.  The  different  kinds  of  plants  that  die  down 
to  the  root  in  autumn  are  what  per  cent  of  the 
whole  number  of  different  kinds? 

4.  The   different  kinds  of   plants  that   die,  root 
and  stem,   in  autumn,   are  what  per   cent  of  the 
whole  number  of  different  kinds? 

5.  The  different  kinds  of  plants  that  live  through 
the  winter  are  what  per  cent  of  the  whole  number 
of  different  kinds  ? 

(>.  The  different  kinds  of  plants  that  produce 
both  seeds  and  buds  are  what  per  cent  of  the 
whole  number  of  different  kinds  ?  „ 

7.  The  different  kinds  of  plants  that  begin  winter 
without  having  formed  seeds  are  what  per  cent  of 
the  whole  number  of  different  kinds? 

8.  The  evergreens  are  what  per  cent  of  the  per- 
ennials ? 

9.  The    perennials   are    what   per   cent    of   the 
entire  number  of  different  kinds  of  plants? 

10.  The  biennials  are  what  per  cent  of  the  entire 
number  of  different  kinds  of  plants? 

11.  The  annuals  are  what  per  cent  of  the  entire 
number  of  different  kinds  of  plants? 

12.  The  annuals  equal  what  percent  of  the  per- 
ennials? 

13.  The  biennials  equal  what  per  cent  of  the  per- 
ennials? 

14.  The  biennials  equal  what  per  cent  of  the 
annuals  ? 


PHYSICS. 


HEAT— EXPANSION  OF  METALS. 

It  is  not  easy  to  devise  apparatus,  simple  enough 
for  use  in  the  public  schools,  which  will  be  worth 
much  in  obtaining  quantitative  results  in  this  study 
of  heat.  Something,  however,  may  be  done  with 
the  following  in  showing  the  linear  expansion  of 
metal  wires  or  rods.  Construct  a  light  wooden 
frame  having  a  bottom  piece  about  thirty  centimeters 
long  by  eight  in  width,  with  an  upright  piece  at  each 
end  of  the  same  width  and  about  fifteen  centimeters 
high.  Place  one  upright,  which  we  will  designate 
A,  with  its  greatest  width  across  the  end  of  the  bot- 
tom strip,  and  the  other,  designated  B,  on  the 
opposite  end  of  the  bottom,  but  with  its  greatest  width 
lengthwise  with  it.  Near  the  top  of  A,  and  in  the  face 
next  to  B,  bore  a  hole  partly  through  large  enough 
to  receive  the  rod  to  be  tested.  At  the  same  bight 

O 

in  B,  and  in  one  of  the  broad  faces,  insert  a  small 
screw-eye.  One  end  of  the  rod  rests  against  the 
back  of  the  hole  in  A  and  the  other  passes  through 
the  screw-eye  in  B.  To  the  face  of  B,  and  in  contact 
with  the  end  of  the  rod,  attach  a  piece  of  steel 
spring  (a  worn-out  watch-spring  straightened  will 
do)  and  allow  it  to  reach  down  nearly  to  the  bottom 
of  the  upright.  Behind  the  lower  end  of  the  spring 

156 


November]  PHYSICS.  15? 

on  the  face  of  B  tack  a  small  arc  of  a  circle  upon 
which  degrees  have  been  marked.  Note  the  degree 
mark  at  which  the  spring  stands  when  the  cold  rod 
is  in  place  and  in  contact  with  it.  Place  a  lamp 
under  the  middle  of  the  rod  and  shield  the  flame  to 
keep  it  steady.  Note  the  exact  time  that  the  flame 
is  applied  and  the  number  of  spaces  passed  oyer 
by  the  index.  Lay  the  rod  aside,  and  while  it  is 
cooling  try  a  similar  rod  of  different  material,  and 
so  on  till  all  have  been  used.  When  the  first  rod 
is  cool  try  it  again  in  the  same  way,  and  continue 
thus  with  all  the  rest  until  an  average  result  of  at 
least  five  trials  have  been  taken.  Iron,  brass,  and 
copper  rods  may  be  easily  obtained,  and  their  rela- 
tive linear  expansibility  may  thus  be  approximately 
determined. 

PROBLEMS. 
I.     WHOLE  NUMBERS. 

1.  What  was  the  average  number  of  spaces  over 
which  the  heated  iron  rod  moved  the  index? 

2.  What  was  the  average  number  of  spaces  over 
which  the  heated  copper  rod  moved  the  index? 

3.  What  was  the  average  number  of  spaces  over 
which  tke  heated  brass  rod  moved  the  index? 

4.  Which  rod  moved  the  index  over  the  greater 
number  of  spaces,  and  how  much,  the  iron  or  the 
copper  ? 

5.  Which  rod  moved  the  index  over  the  greater 
number'  of  spaces,  and  how  much,  the  iron  or  the 
brass? 

6.  Which  rod  moved  the  index  over  the  greater 
number  of  spaces,  and  how  much,  the  copper  or 
the  brass? 


158  NUMBER  WORK.  [November 

7.  Which  rod  moved  the  index  over  the  greatest 
number  of  spaces? 

8.  Which  rod  moved   the   index   over  the   least 
number  of  spaces? 

II.  FRACTIONS. 

1.  The  average   number  of  spaces  over   which 
the   heated  iron  rod  moved  the  index  equals  what 
part  of  the   average  number  of  spaces  over  which 
the  copper  rod  moved  it? 

2.  The   average   number  of  spaces  over    which 
the  heated  iron   rod  moved  the  index  equals  what 
part  of  the  average  number  of  spaces  over  which 
the  brass  rod  moved  it? 

3.  The  average  number  of  spaces  over  which 
the  heated  copper    rod    moved   the  index    equals 
what  part  of  the  average  number  over  which  the 
brass  rod  moved  it? 

4.  The   least   average    expansibility    shown    by 
any    one  metal  equals    what  part  of  that  of   the 
greatest  average  expansibility? 

III.  RATIO. 

1.  What  is  the  ratio  of  the  average  number  of 
spaces   through   which  the  heated  iron •> rod  moved 
the  index  to  the   average  number  through  which 
the  heated  copper  rod  moved  it? 

2.  What  is  the  ratio  of  the  average   number  of 
spaces  through   which  the  heated  iron  rod  moved 
the  index  to  the  average  number  through  which 
the  heated  brass  rod  moved  it? 

3.  What  is  the  ratio  of  the  average  number  of 
spaces  through  which  the  heated  copper  rod  moved 


November]  PHYSICS.  159 

the   index  to  the  average   number  through   which 
the  heated  brass  rod  moved  it? 

4.   What    is    the  ratio    of  the   least    degree    of 
expansibility   shown  by   any   rod  to  the  greatest 
degree  shown  by  any  rod? 
IV.     PERCENTAGE. 

1.  The  average  number  of  spaces  through  which 
the  heated  iron  rod  moved  the  index  equals  what 
per  cent  of  the  average  number  through  which  the 
copper  rod  moved  it? 

2.  The  average  number  of  spaces  through  which 
the  heated  iron  rod  moved  the  index  equals  what 
per  cent  of  the  average  number  through  which  the 
brass  rod  moved  it? 

3.  The  average  number  of  spaces  through  which 
the  heated  copper  rod  moved  the  index  equals  what 
per  cent  of  the  average  number  through  which  the 
brass  rod  moved  it? 

4.  The  least  average  expansibility  shown  by  any 
of  the  rods  equals  what  per  cent  of  the  greatest 
expansibility  ? 


METEOROLOGY. 


PROBLEMS. 
I.     WHOLE  NUMBERS. 
A.     Temperature. 

1.  What  is  the  difference  between  the  average 
reading  of  the  thermometer  for  November  and  the 
average  reading  for  October?     For  September? 

2.  What  is  the  difference  between  the   average 
reading  of  the  thermometer  for  November  and  the 
average  reading  for  October  and  September  ? 

3.  What  is  the  difference  between   the   greatest 
range  in  temperature  for  this  month   and  that  for 
October  ?     For  September  ? 

4.  What  is  the  difference  between   the    lowest 
reading  of  the  thermometer  in  November  and  the 
lowest  reading  in  October?      In  September? 

5.  What  is  the  difference  between   the   highest 
reading  of  the  thermometer  in  November  and  the 
highest  reading  for  October?     For  September? 

6.  What  is  the  average  reading  of  the  thermom- 
eter this  month  on  the  rainy  days  ?     On  the  clear 
days? 

7.  What  is  the  average  reading  of  the  thermom- 
eter for  the   days   on   which   the  prevailing  wind 
blew?       How  much    was   this  average    above  or 
below  the  monthly  average? 

160 


November]  METEOROLOGY.  161 

B.  Barometer. 

8.  What  is  the  difference  between  the  average 
night  of    the  barometer   for   November   and  the 
average  hight  for  October?     For  September? 

9.  What  is  the  difference  between  the  greatest 
range  in  the  barometer   for   November,   and  the 
greatest  range  for  October  ?     For  September  ? 

10.  What  is  the  difference  between  the  average 
hight  of    the    barometer    for   November  and  the 
average  hight  for  October  and  September? 

11.  What  is  the  difference  between  the  average 
hight   of    the    barometer  for   the   rainy    days    in 
November  and  the  average  for  the  rainy  days  in 
October?     For  September? 

12.  What  is  the  difference  between  the  average 
hight   of    the  barometer  for   the  clear    days    in 
November  and  the  average  for  the  clear  days  in 
October?     In  September? 

13.  What  is  the  difference  between  the  average 
hight  of  the  barometer  for  the  clear  days  and  the 
average  for  the  cloudy  days  in  November  ?  Between 
the  average  for  clear  days  and  the  average  for  the 
rainy  days? 

C.  Rainy,  Cloudy,  and  Clear  Days. 

14.  What  is  the  difference  between  the  number 
of  rainy  days  in  November  and  the  number  in 
October  ?     In  September  ? 

15.  What  is  the  difference  between  the  number 
of  cloudy  days  in  November  and  the   number  in 
October?     In  September? 

16.  What  is  the  difference  between  the  number 


162  NUMBER  WORK.  [Novembel 

of  clear  days  in  November   and   the  number   in 
October?     In  September? 

17.  What  is  the  difference  between  the  number 
of   rainy  days  and  the  number   of  clear  days  in 
November  ?    Rainy  days  and  cloudy  days  ?    Cloudy 
days  and  clear  days? 

18.  What  is  the  difference  between  the  number 
of  cloudy  days  without  rain  in  November  and  the 
number  of  cloudy  days  without  rain  in  October? 
In  September? 

D.  Rainfall* 

19.  Which   had  the  greater  rainfall,   and   how 
much,  November  or  October?     November  or  Sep- 
tember? 

20.  Which    had   the  greater  rainfall,  and  how 
much,  November  or  October  and  September  ? 

21.  At  the  November  rate  what  would  be  the 
rainfall  for  a  year? 

22.  What  was  the  daily  average  rainfall  for  the 
month?     Which  is  greater,    and  how    much,    the 
daily  average  rainfall  for  November,  or  the  aver- 
age for  October?     For  November  or  September? 

23.  Which  is  greater,  and  how  much,  the  daily 
average   rainfall  for  the  rainy  days  in    November 
or  the  daily  average  for   October?     In   November 
or  September? 

24.  Which  is  greater,  and  how  much,  the  daily 
average  rainfall  for  the  cloudy  days   in  November 
or  the  daily  average  for  October?     For  November 
or  September? 

E.  Dew,  Frost,  Fogs. 

25.  Which  is  greater,  and  how  much,  the  num- 


November]  METEOROLOGY.  163 

her    of    dews    in     November  or  the    number  in 
October?     In  November  or  September? 

26.  Which  is  greater,  and  how  much,  the  num- 
ber   of  frosts  in   November    or    the  number    in 
October?     In  November  or  September? 

27.  Which  is  greater,  and  how  much,  the  num- 
ber of  foggy  mornings  in  November  or  the  number 
in  October?     In  November  or  September? 

28.  How     many    more    frosts    than    dews    in 
November  ? 

II.     FRACTIONS. 
A .     Te  mpera  ture. 

1.  The  average  reading  of  the  thermometer  for 
November  equals  what  part  of  the  average  reading 
for  October?     For  September? 

2.  The  average  reading  of  the  thermometer  for 
November  equals  what  part  of  the  average  read- 
ing for  October  and  September? 

3.  The  greatest  range  of  temperature  in  Novem- 
ber equals  what  part  of  the  greatest    range    for 
October?     For  September? 

4.  The  lowest  reading  of  the  thermometer  for 
November  equals  what  part  of  the  lowest  reading 
for  October?     For  September? 

5.  The  highest  reading  of  the  thermometer  for 
November  equals   what  part  of  the    highest    for 
October?     For  September? 

6.  The  average  reading  of  the  thermometer  for 
the  rainy  days  equals  what  part  of  the   average 
reading  for  the  clear  days  ? 

7.  The  average  reading  of  the  thermometer  for 
the  days  on  which  the  prevailing  wind  blew  equals 
what  part  of  the  monthly  average  ? 


164  JV 'UMBER  WORK.  [November 

13.     Barometer. 

8.  The    average     hight  of     the   barometer  for 
November  equals  what  part  of  the  average  hight 
for  October  ?     For  September  ? 

9.  The  greatest  range  of  barometer  for  Novem- 
ber equals   what  part  of  the    greatest    range   for 
October?     For  September? 

10.  The  average  barometer  reading  for  Novem- 
ber equals   what  part  of  the  average  for  October 
and  November? 

11.  The  average  hight  of  the  barometer  for  the 
rainy  days  in  November  equals  what  part  of  that 
for  the  rainy  days  in  October  ?     In  September  ? 

12.  The  average  hight  of  the  barometer  for  the 
clear  days  in  November  equals  what  part  of   the 
average  hight  for  the  clear  days  in  October?     In 
September? 

13.  The  average  hight  of  the  barometer  for  the 
rainy  days  in  November  equals  what  part  of  the 
average  for  the  clear  days? 

14.  The  average  hight  of  the  barometer  for  the 
rainy  days  equals  what  part  of  the  average  hight 
for  the  cloudy  days? 

C.     Rainy ,  Cloudy,  and  Clear  Days. 

15.  The  number  of   rainy  days   in   November 
equals  what  part  of  the  number  of  rainy  days  in 
October?     In  September? 

16.  The    number  of   clear   days  in    November 
equals  what   part  of  the  number  of  clear  days  in 
October?     In  September? 

17.  The  number  of  cloudy  days  in  November 


November]  METEOROLOGY.  165 

equals  what  part  of  the  number  of  cloudy  days  in 
October?     In  September? 

18.  The  number  of  cloudy  days  in  November 
equals  what  part  of  the  number  of  clear  days  ? 

19.  The  number  of  rainy  days  equals  what  part 
of  the  number  of  cloudy  days  in  November? 

20.  The  number  of  cloudy  days  without  rain  in 
November  equals  what  part  of  the  number  without 
rain  in  October?     In  September? 

21.  At  the  November  rate,  how  many  rainy  days 
would  there  be  in  a  year?     Cloudy  days?     Clear 
days? 

D.     Rainfall. 

22.  The  rainfall  in  November  equals  what  part 
of  the  rainfall  for  October?     For  September? 

23.  The  rainfall  for  November  equals  what  part 
of  the  rainfall  for  October  and  September  ? 

24.  The  daily  average  rainfall  for  the  rainy  days 
in  November  equals  what  part  of  the  daily  average 
for  the  rainy  days  in  October?     In  September? 

25.  The  daily  average  rainfall   for  the  cloudy 
days  in  November  equals  what  part  of  -the  daily 
average  for  the  cloudy  days  in  October?     In  Sep- 
tember ? 

26.  The   daily   average   rainfall   for   the  month 
equals  what  part  of  the  daily  average  for  the  rainy 
days? 

K     Dew,  Frost,  Fogs. . 

27.  The  frosty  mornings  equal  what  part  of  the 
month  ? 

2S.   The   mornings  with   fog  equal  what  part  of 
the  month? 


166  NUMBER  WORK.  [November 

29.  The  mornings  with  dew  equal  what  part  of 
the  month? 
III.     RATIO. 

A.     Temperature. 

1.  What  is  the  ratio  of   the   average  reading  of 
the   thermometer  for   November    to    the    average 
reading  for  October?     To  that  for  September? 

2.  What  is  the  ratio  of  the   average  reading   of 
the    thermometer   for  November   to    the    average 

o 

reading  for  October  and  September? 

3.  What  is  the  ratio  of  the  greatest  range  of 
temperature  in    November  to   the  greatest   range 
in  October?     In  September? 

4.  What  is  the   ratio  of  the   lowest   reading  of 
the  thermometer  in  November  to  the  lowest  read- 
ing in  October?     In  September? 

5.  What  is  the  ratio  of  the  highest   reading   of 
the  thermometer  in  November  to  the  highest  read- 
ing in  October  ?     In  September? 

6.  What  is  the  ratio  of  the   average   reading  of 
the  thermometer  on  the   rainy  days   in  November 
to  the  average  for  the  rainy  days  in  October?     In 
September? 

7.  What  is  the  ratio  of  the  average  reading  of 
the  thermometer  on  the  clear  days  in   November 
to  the  average  for  the  clear  days   in  October  ?     In 
September  ? 

8.  What  is  the  ratio  of  the  average  reading  of 
the  thermometer  for  the  cloudy  days  to   the    aver- 
age for  the  clear  days  in  November? 

9.  What  is  the  ratio  of  the   average  reading  of 
the  thermometer  at  which  rain  fell  to  that  at  which 
snow  fell  during  the  month  ? 


November]  .17  /•;  rEOROLOG  Y.  167 

B      Barometer. 

10.  What  is  the  ratio  of  the  average  hight  of 
the  barometer  for  November  to  the  average  for 
October?  For  September? 

1L  What  is  the  ratio  of  the  greatest  range  in 
the  hight  of  tiie  barometer  in  November  to  the 
greatest  range  in  October?  In  September? 

12.  What  is  the  ratio  of  the   average  hight    of 
the  barometer  for  the  rainy   days   to   the  average 
hight  for  the  clear  days  ? 

13.  What  is  the  ratio  of  the   average  hight  of 
the  barometer  on  the  rainy  days  to   the  average 
hight  for  the  cloudy  days  without  rain? 

14.  What  is  the  ratio  of  the  average    hight  of 
the  barometer  for  the  rainy  days  in  November  to 
the  average  hight  for  the  rainy  days  in   October? 
In  September? 

15.  What  is  the  ratio  of  the   average   hight  of 
the  barometer  for  the  clear  days  in  November  to 
the  average  for  the  clear   days  in  October?     In 
September  ? 

16.  What  is  the  ratio  of  the  average   hight  of 
the  barometer   for  the  days  with    less    than    the 
average  temperature  to  that  with  the  days  having 
more  than  the  average  temperature  ? 

C.     Rainy,  Cloudy,  and  Clear  Days. 

17.  What    is    the    ratio   of  the    rainy    days    in 
November  to  the  number  in  October?     In  Septem- 
ber? 

18.  What  is  the  ratio  of  cloudy  days  in  Novem- 
ber to  the  number  in  October?     In  September? 

19.  What    is   the    ratio   of  the   clear   days    in 


1G3  NUMBER  WORK.  [November 

November  to  the  number  in  October?     In  Septem- 
ber? 

20.  What  is  the  ratio  of  rainy    days   to    clear 
days  in  November? 

21.  What   is  the   ratio  of  rainy  days  to  cloudy 
days  in  November? 

22.  According   to    the    November    ratio,    what 
would  be  the  number  of  cloudy   days  in  a  year? 
The  number  of  clear  days? 

23.  According   to    the    November    ratio,    what 
would  be  the  number  of  rainy  days  in  a  year? 

D.     Rainfall. 

24.  What  is  the   ratio  of  the  November  rainfall 
to  the  rainfall  for  October?     For  September? 

25.  What  is  the  ratio  of  the  daily  average  rain- 
fall  for  the  rainy  days  in  November  to  the  daily 
average    for    the    rainy    days    in    October?     For 
September  ? 

26.  What  is  the  ratio  of  the  daily  average  rain- 
fall for  the  cloudy  days  in  November  to  the  daily 
average    for   the    cloudy    days    in    October?      In 
September  ? 

27.  What  is  the  ratio  of  the  daily  average  rain- 
fall for  the  rainy   days  in  November  to  the  daily 
average  for  the  cloudy  days  ? 

28.  What  is  the    ratio  of  the  rainfall    on    the 
days  when  the  barometer  stood  below  the  average 
hight   to  the   average   for   the  days  when  it  stood 
above  the  average  hight  ? 

29.  What  is  the  ratio  of  the  rainfall  on  the  days 
when    the    temperature    was   below    the    monthly 
average  to  that  for  the  days  when  the  temperature 
was  above  the  average? 


November]  METEOROLOGY.  169 

E.     Dew,  Frost,  Fog. 

30.  What  is  the  ratio  of  the  dewy  mornings  to 
those  with  frost  ? 

31.  What  is  the  ratio  of  the  clear  mornings  to 
those  with  fogs? 

IV.     PERCENTAGE. 
A.     Temperature. 

1.  The  average  reading  of  the  thermometer   for 
November  equals  what  per  cent  of    the  average 
reading  for  October?     For  September? 

2.  The  average  reading  of  the  thermometer   for 
November  equals  what  per  cent  of  the    average 
reading  for  October  and  September? 

3.  The     greatest    range     of   temperature    for 
November  equals  what  per  cent  of  the  greatest 
range  for  October?     For  September ? 

4.  The  lowest  reading  of  the  thermometer  for 
November   equals  what   per   cent  of    the    lowest 
reading  for  October?     For  September? 

5.  The  highest  reading  of  the  thermometer  for 
November  equals  what  per  cent  of  the   highest 
reading  for  October?     For  September? 

6.  The  average  reading  of  the  thermometer  for 
the  rainy  days  equals  what  per  cent  of  the  average 
reading  for  the  clear  days? 

7.  The  average  reading  of  the  thermometer  for 
the  rainy  days  in  November  equals  what  per  cent 
of    the   average    reading    for    the   rainy    days   in 
October?     In  September? 

8.  The  average  reading  of  the  thermometer   for 
the  days  when  it  snowed  equals  what   per  cent  of 
the  average  for  the  rainy  days? 


170  NUMBER  WORK,  [November 

B.  Barometer. 

9.  The    average    hight    of  the    barometer    for 
November  equals   what   per  cent  of  the   average 
hight  for  October?     For  September? 

10.  The  greatest  range  in  barometric  hight  for 
November  equals   what  per  cent  of  the   greatest 
range  for  October?     For  September? 

11.  The  average  barometric  hight  for  the  rainy 
days  in  November  equals   what   per  cent   of  the 
average  for  the  rainy  days  in  October?     In  Sep- 
tember? 

12.  The    average    barometric  reading    for    the 
clear  days  in  November  equals  what  per  cent  of 
the   average   for  the  clear  days  in   October?     In 
September  ? 

13.  The  average  reading  of  the  barometer  for 
the  rainy  days  in  November  equals  what  per  cent 
of  the  average  for  the  clear  days? 

14.  The  average  hight  of  the  barometer  for  the 
rainy  days  in  November  equals  what  per  cent  of 
the  average  for  the  cloudy  days? 

C.  Rainy,  Cloudy,  and  Clear  Days. 

15.  The  number  of   rainy    days   in    November 
equals  what  per  cent  of  the  number  of  rainy  days 
in  October?     In  September? 

16.  The    number  of  clear   days    in    November 
equals  what  per  cent  of  the  number  of  clear  days 
in  October?     In  September? 

17.  The  number  of  cloudy  days   in   November 
equals    what  per    cent  of  the    number  of  cloudy 
days  in  October?     In  September? 

18.  The  number  of  snowy  days  in  November 


November]  METEOROLOGY.  171 

equals  what' per  cent  of  the  number  of  cloudy  days 
in  November? 

19.  The   number  of  rainy    days   in    November 
equals    what   per  cent   of    the  number  of  cloudy 
days? 

20.  The  number  of  rainy  days   in    November, 
when  the  barometer  was  below  the  monthly  aver- 
age, equals  what  per  cent  of  the  entire  number  of 
rainy  days? 

21.  The  number  of  cloudy  days  without  rain  in 
November   equals    what    per   cent    of    the    entire 
number  of  cloudy  days  ? 

22.  At  the  November  rate,  how  many  rainy  days 
would  there  be  in  a  year?     Cloudy  days?     Clear 
days? 

D.     Rainfall. 

23.  The  rainfall  for  November  equals  what  per 
cent  of  the  rainfall  for  October?    For  September? 

24.  The  rainfall  for  November  equals  what  per 
cent  of  the  rainfall  for  October  and  September? 

25.  At  the  November  rate,  what  would  be  the 
rainfall  for  a  year? 

26.  The  •  daily    average    rainfall    in    November 
equals   what    per  cent  of    the    daily  average    for 
October?     For  September? 

27.  The  daily  average   rainfall  for  the  cloudy 
days  in  November  equals  what  per  cent  of  that  for 
the  cloudy  days  for  October?     For  September? 

28.  The  daily  average  rainfall  for  the  rainy  days 
in  November  equals  what  per  cent  of  that  for  the 
rainy  days  m  October?     In  September? 

2(J.  The  daily  average  rainfall  for  the  month  of 


172  NUMBER  WORK.  [November 

November  equals   what  per  cent  of  that  for  the 

rainy  days? 

K    Dew,  Frost,  Fogs. 

30.  The  mornings  with  dew  equal  what  per  cent 
of  the  whole  number  in  the  month? 

31.  The  mornings  with  fog  equal  what  per  cent 
of  the  whole  number  in  the  month  ? 

32.  The  mornings  with  frost  equal  what  per  cent 
of  the  whole  number  in  the  month  ? 


METEOROLOGY-AUTUMN    MONTHS. 

PROBLEMS. 

A.  Temperature. 

1.  What  is  the  average  reading  of  the  thermom- 
eter for  the  autumn  months? 

2.  What  is  the  greatest   range  in  temperature 
during  autumn? 

3.  What  is  the  average  reading  of  the  thermom- 
eter for  the  rainy  days? 

4.  What  is  the  average  reading  of  the  thermom- 
eter for  the  clear  days? 

5.  What  is  the  greatest  range  of  temperature  for 
the  rainy  days? 

6.  What  is  the  greatest  range  of  temperature 
for  the  clear  days? 

7.  The  average  reading  of  the  thermometer  for 
the  cloudy  days  equals  what  part  of  the  average 
for  the  clear  days? 

8.  The  average  reading  of  the  thermometer  for 
the  rainy  days  equals  what  part  of  the  average  for 
the  clear  days? 

9.  What  part  of  the  season  had  passed  before 
the  lowest  temperature  was  reached?    The  highest 
temperature  ? 

B.  Barometer. 

10.  What  is  the  average  hight  of  the  barometer 
for  autumn  ? 

173 


174  NUMBER  WORK.  [November 

11.  What  is  the  greatest  barometric  range  in 
autumn? 

12.  The  average  reading  of  the  barometer  for 
the  rainy  days  equals  what   part  of  that   for  the 
clear  days? 

13.  The  average  reading  of  the  barometer  for 
the  cloudy  days  equals  what  part  of  the  average 
for  the  clear  days? 

14.  The  average  reading  of  the  barometer  when 
the  temperature  was  below  the  average  for  the  sea- 
son equals  what  part  of  the  average  reading  when 
the  temperature  was  above? 

C.  Rainy,  Cloudy,  and  Clear  Days. 

15.  How  many  rainy  days  in  autumn? 

16.  At  the  autumn  rate  what  part  of  the  entire 
year  would  be  rainy?     How  many  rainy  days? 

17.  At  the  autumn  rate  how  many  cloudy   days 
would  there  be  in  a  year?     Clear  days? 

18.  What  part  of  the  entire  number   of  cloudy 
days  were  rainy  days? 

19.  What   per   cent    of  the    cloudy    days    were 
without  rain  or  snow  ? 

D.  Rainfall. 

20.  What  is  the  total  rainfall  for  autumn  ? 

21.  At  the  autumn  rate  what  would  be  the  total 
rainfall  for  a  year? 

22.  What  is  the  average  rainfall  for  each  day  in 
autumn  ? 

23.  What  is  the  average  rainfall  for  each  rainy 
day  in  autumn? 

24.  What  is  the  average  rainfall  for  each  cloudy 
day  in  autumn? 


November]  METEOROLOGY.  175 

25.  What  part  of  the  rainfall  occurred  with  the 
barometer  below  the  average  hight?     Above  the 
average  ? 

26.  What  part  of  the  rainfall  occurred  when  the 
temperature  was  above  the  average?     Below  the 
average  ? 


ASTRONOMY. 


VARIATION  IN  DAY'S  LENGTH. 

I.     WHOLE  NUMBERS. 

1.  What    is  the  variation  in   the   day's  length 
during    the    first    week?     During    the    second? 
During  the  third?     During  the  fourth? 

2.  What  is   the   variation    in  the  day's  length 
during  the  month? 

3.  What  is  the  variation  in  the  day's   length  in 
the  morning  during  the  first  week?     The  second? 
The  third  ?     The  fourth  ?     For  the  entire  month  ? 

4.  What  is  the  evening  variation  in   the  day's 
length  during  the  first  week?     The  second?     The 
third  ?     The  fourth  ?     For  the  entire  month  ? 

5.  Which  is  the   greater,   and   how   much,  the 
variation    in    the    day's    length    during   the   first 
week  or  the  variation  during  the  last  week? 

6.  What  is  the  difference  between  the  variation 
in  the  day's  length  in   the  morning  and  the  varia- 
tion in  the  evening  during  the  first   week  ?     Dur- 
ing the  second  ?     During  the  third  ?     During  the 
fourth?     During  the  entire  month? 

7.  How  many  degrees  on  the  meridian   did  the 
sun  pass  through  during  the  month  ?     During  each 

week? 

176 


Xnvmber]  ASTRONOMY.  177 

8.  What  was  the  difference  between  the  length 
of  the   day   and  the  length   of   the    night   at    the 
beginning  of  the  month?     At  the  end? 

9.  What  is  the  difference  between  the  length  of 
the  last  day  in  November   and  the   length  of  the 
first  day  in  September? 

10.  What  is  the    difference  between   the  varia- 
tion   in  the  day's    length  in   November  and    the 
variation  in  October  ?     In  September  ? 

11.  What  is  the  difference  between  the  morning 
variation  in  the  day's  length    in   November    and 
the  morning  variation  in  October  ?   In  September  ? 

12.  What  is  the  difference   between  the  evening 
variation  in  the   day's   length   during  November 
and  the  evening  variation  during   October?     Dur- 
ing September? 

13.  What  is  the  difference  between  the  morning 
and  the  evening  variation  in  the  day's  length  dur- 
ing the  three    months — November,  October,  and 
September  ? 

14.  What  is  the  difference  between  the  variation 
in    the   day's    length    during    the    last    week    in 
November  and  the  variation  during  the   first  week 
in  September? 

5.  What  is  the  difference,  in  degrees  on  the 
meridian,  between  the  movement  of  the  sun  in 
November  and  that  during  October?  During 
September? 

16.  What  is  the  difference,  in  degrees  on  the 
meridian,  between  the  movement  of  the  sun  during 
the  last  week  in  November  and  the  movement  dur- 
ing the  first  week  in  September? 


178  NUMBER  WORK.  [November 

17.  What  is  the  difference  between  the    area  of 
the  cross-section  of  the  shadow-stick  and   that   of 
the    shadow    cast    the    first    week    of   November? 
The  second  week?     The  third  week?     The  fourth 
week? 

18.  What  is  the  difference  in  area  between   the 
shadow  cast  the  first  week  in  November  and  that 
cast  the  last  week? 

19.  What  is  the  difference  in  area  between  the 
shadow  cast  the  first  week  in  September    and  that 
of  the  last  week  in  November? 

II.     FRACTIONS. 

1.  The  variation  in  the  day's  length  during  the 
first   week  in   November  equals  what  part  of  its 
length    at  the    first   of    the    week?     During   the 
second?     During  the  third?     During  the  fourth? 

2.  The  entire  variation  in  the  day's  length  dur- 
ing the   month   equals  what  part  of  the  length  of 
the  first  day  of  the  month? 

3.  The   variation  in  the   day's   length,    in    the 
morning,  during  the  first  week  equals  what  part 
of  the  total  variation  ?     During  the  second  ?    Dur- 
ing the  third?     During  the  fourth? 

4.  The   variation    in   the    day's    length,  in  the 
evening,  during  the  first  week  equals  what  part  of 
the  total  variation?     During    the   second    week? 
During    the    third   week?       During    the    fourth 
week  ? 

5.  The  variation  in  the  day's  length,  in  the  morn- 
ing, daring  the  first  week  equals  what  part  of  the 
variation  in  the  evening  for  the  same  time  ?     The 
second  week?    The  third  week?    Tho  fourth  week? 


November]  ASTRONOMY.  170 

0.  The  variation  in  the  length  of  the  day,  in  the 
morning,  during  the  month  equals  what  part  of 
the  entire  amount  of  variation? 

7.  The  variation  in  the  length  of  the  day,  in  the 
evening,  during  the  month  equals  what  part  of  the 
entire  amount  of  variation? 

8.  The  variation  in  the  length  of  the  day,  in  the 
morning,  during   the   month  equals  what  part  of 
the  variation  in  the  evening? 

9.  The    variation    in    the    day's    length    during 
November  equals  what  part  of  the  variation  dur- 
ing October?     September? 

10.  The  variation  in  the  day's  length  during  the 
last  week  in  November  equals  what    part  of  the 
variation  during  the  first  week  in  September? 

11.  The  variation  in    the  day's  length,  in  the 
morning,  during  November  equals  what  part  of  the 
variation  for  the  same  time  in  October?     In  Sep- 
tember? 

12.  The   variation  in  the  day's  length,  in  the 
evening,  during  November  equals  what  part  of  the 
variation    for   the    same    time    during    October? 
During  September? 

13.  The  morning  variation  in  the  day's  length 
for   the    three    months,   November,   October,   and 
September,  equals  what  part  of  the  entire  amount 
of  variation  for  the  same  time? 

14.  The  evening  variation  in  the  day's  length 
for  the    three    months,    November,    October,  and 
September,  equals  what  part  of  the  entire  amount 
of  variation? 

15.  The    morning   variation    during    the    three 


180  NUMBER  WORK.  [November 

months,  November,  October,  and  September,  equals 
what  part  of  the  evening  variation' for  the  same 
time? 

16.  The  number  of  degrees    on    the    meridian 
through  which   the  sun  passed  during  November 
equals   what  part  of  the   number  passed  through 
during  the  three  months,  November,  October,  and 
September?     During  October?     During  Septem- 
ber? 

17.  The  area  of  the  cross-section  of  the  shadow- 
stick  equals  what   part  of  the  area  of  the  shadow 
cast  the  first  week  in  November? 

18.  The  area  of  the  shadow  cast  the  first  week 
in  November  equals  what  part  of  the  area  of  the 
shadow  cast  the  second?    The  third?    The  fourth? 

19.  The  area  of  the  shadow  cast  the  first  week 
in  September  equals  what  part  of  the  area  of  the 
shadow  cast  the  last  week  in  November? 

III.     RATIO. 

1.  What  is  the  ratio  of  the  variation  in  the  day's 
length   during  the  first  week  to  the  variation  for 
the  entire   month  ?     During  the  second  ?     During 
the  third?     During  the  fourth ? 

2.  What  is    the    ratio    of  the    variation  in  the 
day's  length  during  the  first  week  to  the  variation 
during  the  last  week  ? 

3.  What  is  the  ratio  of  the  morning  variation 
in  the  day's  length  during  the  first  week   to  the 
entire  variation   during  the  week?     The   second? 
The  third?     The  fourth? 

4.  What  is  the  ratio  of  the  evening  variation  in 
the  day's  length  during  the  first  week  to  the  entire 


Nmvmber]  ASTRONOMY.  181 

variation   during   the   week?     The   second?     The 
third?     The  fourth? 

5.  What  is  the  ratio  of  the  morning  variation  in 
the  day's  length  during  the  first  week  to  the  even- 
ing  variation    in    the    same    time?      During   the 
second  week?     During  the  third  week?     During 
the  fourth  week? 

6.  What  is  the  ratio  of  the  morning  variation  in 
the  day's  length  during  the  month  to  the  evening 
variation  durmg  the  same  time? 

7.  What  is  the  ratio  of  the  morning  variation  in 
the   day's   length  during  the  month  to  the   entire 
variation  during  the  month  ? 

8.  What  is  the  ratio  of  the  evening  variation  in 
the  day's  length  during  the  month  to  the  entire 
variation  during  the  month? 

9.  What  is  the  ratio,   in  length,  of  November 
30th  to  September  1st? 

10.  What  is  the  ratio  of  the  variation  in  the 
day's  length  during  the  last  week  in  November  to 
the  variation  during  first  week  in  September  ? 

11.  What  is   the  ratio  of  the  variation  in  the 
day's  length  during  November  to  the  variation  in 
September  ?     October  ? 

12.  What  is  the  ratio  of  the  morning  variation 
in  the  day's  length  during  November  to  the  morn- 
ing variation  during  October?     September? 

13.  What  is  the  ratio  of  the  evening  variation 
in  the  day's  length  during  November  to  the  even- 
ing variation  during  October?     September? 

14.  What  is  the  ratio  of  the  morning  variation 
in   the   day's   length   during   November,  October, 


182  NUMBER  WORK.  [November 

and  September  to  the  evening  variation  during  the 
same  time? 

15.  What    is    the    ratio    of    the    movement,   in 
degrees,  of  the  sun  on  the  meridian  during  Novem- 
ber to  the  movement  during  October?  September? 

16.  What   is  the  ratio  of  the  movement  of  the 
sun,  in  degrees,  on  the  meridian   during  the  last 
week  in  November  to  the  movement  during    the 
first  week  in  September? 

17.  The  area  of  the  cross-section  of  the  shadow- 
stick   bears  what   ratio  to  the  area  of  the   shadow 
cast   the   first   week    in   November?     The  second 
week?     The  third  week?     The  fourth  week? 

18.  The  area  of  the  shadow  cast  the  first  week 
bears  what  ratio  to  the  area  of  the  shadow  cast  the 
second  ?     The  third  ?     The  fourth  ? 

19.  The   area  of  the  shadow  cast  the  first  week 
in  September  bears  what  ratio  to  the  area  of  the 
shadow  cast  the  last  week  in  November? 

IV.  PERCENTAGE. 

1.  What  per  cent  of  the   day's   length    at  the 
beginning  of  the  week  was  lost  or  gained  during 
the  first  week?     During  the  second?     During  the 
third  ?     During  the  fourth  ? 

2.  What  per  cent  of  the   day's   length   at  the 
beginning  of  the  month  was  gained  or  lost  during 
the  entire  month? 

3.  What  per  cent   of  the   gain    or  loss  of  the 
day's  length  during  the  first  week  occurred  in  the 
morning?     During  the  second  week ?     During  the 
third  week?     During  the  fourth  week? 

4.  What  per  cent  of  the  gain  or  loss  in  the  day's 


November!  ASTRONOMY.  183 

length  during  the  first  week  occurred  in  the  even- 
ing? During  the  second  week?  During  the 
third  week?  During  the  fourth  week? 

5.  The  gain  or  loss  in  the  day's  length  in  the 
morning  during  the  month   equals  what   per  cent 
of  the  gain  or  loss  in  the  evening? 

6.  The  gain  or  loss  in  the  day's  length  during 
the  first  week  equals  what  per  cent  of  the  gain   or 
loss  during  the  last  week? 

7.  The  movement,  in  degrees,  of  the  sun  on  the 
meridian  during  the  last  week   equals  what  per 
cent  of  the  movement  during  the  first  week? 

8.  The  gain  or  loss  in  the  day's  length   during 
November  equals  what  per  cent  of  the  gain  or  loss 
during  October?     September? 

9.  The  gain  or  loss  in  the  day's  length  during 
the  last  week  in  November  equals  what  per  cent 
of  the  gain  or  loss  during  the  first  week  in  Sep- 
tember ? 

10.  The  gain  or  loss  in  the  day's  length,  in  the 
morning,  during  November  equals  what  per  cent 
of  the  gain  or  loss  during  October?     September? 

11.  The  gain  or  loss  in  the  day's  length,  in  the 
evening,  during  November  equals  what    per  cent 
of   the   gain  or  loss    for   the    same   time    during 
October?     During  September? 

12.  The  variation  in  the  length  of  the  day  dur- 
ing November  equals  what  per  cent  of  the  varia- 
tion   for   the  three    months,  November,   October, 
September? 

13.  The  morning  variation  in  the  day's  length 
for  the  three  months  equals  what  per  cent  of  the 
total  variation  for  that  time  ? 


184  NUMBER  WORK.  [November 

14.  The   number  of  degrees    on    the    meridian 
through  which  the  sun  passed  during  November 
equals    what    per    cent   of    the    number    passed 
through  in  October?     September? 

15.  The    number  of  degrees  on    the    meridian 
through  which  the  sun  passed  during  the  last  two 
weeks  of  the  month  equals  what  per  cent  of  the 
number  passed  through  during  the  first  two  weeks 
of  September? 

16.  The   number  of  degrees    on  the    meridian 
through   which  the  sun  passed  in  October  equals 
what  per  cent  of  the  number  passed  through  in  the 
three  months,  November,  October,  and  September? 

17.  The  area  of  the  cross-section  of  the  shadow- 
stick   equals    what   per   cent  of   the    area  of  the 
shadow  cast  the  first  week  in  November? 

18.  The  area  of  the  shadow  cast  by  the  shadow- 
stick  the  first  week  in  November  equals  what    per 
cent  of  the  area  of  the   shadow  cast   the   second? 

.The  third?     The  fourth? 

19.  The  area  of  the  shadow  cast  the  first  week 
in  September  equals  what  per  cent  of  the  area  of 
the  shadow  cast  the  last  week  in  November  ? 


GEOGRAPHY. 


NORTH   AMERICA-ZONES  AND  CLIMATE. 

It  is  the  aim,  by  means  of  the  problems  given 
under  this  head,  to  fix  in  the  minds  of  the  pupils 
definite  ideas  of  those  great  zones  whose  bound- 
aries seem  to  be  determined  by  certain  phases  of 
animal  and  plant  life  rather  than  by  mathematical 
lines.  The  variation  of  these  zones  from  those 
dependent  upon  the  mathematical  relations  of  the 
earth  to  the  sun  may  be  taken  as  a  measure  of  the 
effect  of  the  influences  of  physical  features  upon 
astronomical  climate.  It  is  a  phase  of  the  study  of 
geography  which  underlies,  fundamentally,  the  study 
of  life  distribution  (to  be  considered  later)  and  with 
this  in  mind  it  becomes  a  subject  of  surpassing 
interest. 

Guyot  gives  six  Zones  of  Vegetation  which  are 
bounded  approximately  by  isothermal  lines  as  follows: 

(a)  North  Polar  Zone;  mean  temperature,  below 
5°  Fahr. 

(5)  Arctic  Zone;  mean  temperature,  5°  to  30° 
Fahr. 

(c)  Cold  Temperate  Zone;  mean  temperature,  30° 
to  40°  Fahr. 

(<7.)  Temperate  Zone;  mean  temperature,  40°  to 
60°  Fahr. 

185 


186  NUMBER  WORK.  [November 

(e)  Warm  Temperate  Zone;  mean  temperature, 
60°  to  72°  Fahr. 

(/)  Tropical  Zone;  mean  temperature,  72°  to  82° 
Fahr. 

The  various  areas  required  in  the  following  prob- 
lems, when  they  are  not  directly  given,  may  be 
found  by  adding  together  the  areas  of  the  different 
political  divisions.  By  these  exercises  it  is  intended 
to  lay  a  foundation  for  a  definite  .understanding  of 
the  relative  productiveness  of  the  different  regions 
of  the  continent. 

PROBLEMS. 
I.  WHOLE  NUMBERS. 

1.  How  many  square  miles  in  each  of  the  zones 
given  above? 

2.  Which    zone    includes   the   largest    area   in 
North  America,  and  how  much  ? 

3.  Which  zone  has  the  smallest  area  in   North 
America,  and  how  much? 

4.  Which  is   larger,  and   how   much,  the  area 
included  in  the  two  temperate  zones  or  the  area  of 
the  tropical  zone? 

5.  Which  includes  a  larger  area  of  the  continent, 
and  how  much,   the  cold  temperate  zone   or  the 
temperate  zone? 

6.  Which  includes  the  greater  area  of  the  con- 
tinent, and  how  much,  the  temperate   zone  or  the 
warm  temperate  zone? 

7.  Which  includes  the  greater  area   of  the  con- 
tinent, and  how  much,  the   warm   temperate    zone 
or  the  cold  temperate  zone? 


GEOGRAPHY.  187 


8.  Which  includes  the  greater  area  of  the   con- 
tinent, and  how  much,  the  north  polar  zone  or  the 
Arctic  zone? 

9.  Which  includes  the  greater  area  of  the   con- 
tinent,   and   how   much,  the    Arctic  zone    or  the 
tropical  zone? 

10.  Which  zone  has  the  greatest  average  width 
and  how  much? 

11.  Which  zones  have  the  greater  average  width, 
and  how  much,  the  temperate  zones  or  the  tropical 
zone? 

12.  Which  zone  is  the   wider,  on   the  average, 
and  how  much,  the   cold    temperate   zone   or   the 
temperate  zone  ? 

13.  Which  zone  is  the  wider,  on   the  average, 
and  how  much,  the  temperate   zone  or  the  warm 
temperate  zone? 

14.  Which   is   greater  in    average    width,    the 
north  polar  zone  or  the  Arctic  zone? 

15.  Which    is   greater   in    average    width,  and 
how  much,  the  Arctic  zone  or  the  tropical  zone? 

16.  Which  is  greater,  and  how  much,  the  area 
lying    south,    or   that    lying    north    of  the    mean 
annual  isotherm  of  60°? 

17.  Which  is  the  greater,  and  how   much,  the 
area  lying  south,  or  that  lying  north  of  the  mean 
annual  isotherm  of  50°? 

18.  Which  is  the  greater,  and  how  much,  the 
area    included  between  50°  and  60°  Fahr.,  or  that 
included  between  60°  and  70  '  Fahr.? 

19.  Which  is  greater,  and  how  much,  the   area 
included   between   701  and   80°  Fahr.,  or  that   in- 
cluded between  60°  and  70°  Fahr.? 


188  NUMBER  WORK.  [November 

20.  Which  is  greater,  and  how  much,  the  area 
included  between  40°  and  50°  Pah r.,  or  that  included 
between  30°  and  40°  Fahr.  ? 

21.  What  area,  in  square  miles,  lies  between  the 
mean  July  isotherm  60°  Fahr.  and  the  mean  Janu- 
ary isotherm  of  60°? 

22.  What  is  the  average  distance  that  the  July 
isotherm  60°  Fahr.  lies  north  of  the  mean  annual 
isotherm  60°  Fahr.  ? 

23.  What  is  the  average  distance  that  the  Janu- 
ary   isotherm    60°   Fahr.  lies    south  of  the    mean 
annual  of  60°  Fahr.  ? 

24.  Which  has  the  greater  annual  rainfall,  and 
how  much,  the  area  east  of  the  Mississippi  or  the 
area  west,  within  the  United  States? 

25.  Which    has   the  greater    rainfall,  and   how 
much,  the  area    south  of  the   Ohio   River  or  the 
area  north,  within  the  United  States  and  east  of 
the  Mississippi? 

26.  Which     river    basin   receives     the    greater 
depth  of  rainfall,    and    how    much,    the  Ohio  or 
the  Missouri? 

27.  Which    has    the   greater  depth    of  rainfall 
annually,  and  how  much,  the  Mississippi  basin  or 
the  St.  Lawrence  basin  ? 

28.  Which  receives  the  greater  depth  of  rainfall 
annually,  and  how  much,  the  Atlantic  slope  or  the 
Pacific  slope  ? 

29.  Which  receives  the   greater  depth  of  rain- 
fall annually,  and  how  much,  the  western  highland 
or  the  eastern  highland? 

30.  Which  receives  the  greater  depth  of  rain- 


November]  GEOGRAPHY.  180 

fall  annually,  and  liow  much,  the  eastern  or  the 
western  division  of  the  Mississippi  basin? 

31.  Which  receives  the  greater  depth  of  rain- 
fall annually,  and  how  much,  the  area  north  of 
the  Great  Lakes  or  the  area  south  of  them  ? 

II.     FRACTIONS. 
A.     Zones. 

1.  The    area    included   in  the    temperate    zone 
equals  what  part  of  the  area  of  the  continent? 

2.  The  area   included   in    the  warm  temperate 
zone  equals  what  part  of  the  area  of  the  continent  ? 

3.  The    area   included   in    the    cold    temperate 
zone  equals  what  part  of  the  area  of  the  continent? 

4.  The  area  included  in  the  tropical  zone  equals 
what  part  of  the  area  of  the  continent? 

5.  The  area  included  in  the  Arctic  zone  equals 
what  part  of  the  area  of  the  continent? 

6.  The  area  included  in  the  north  polar  zone 
equals  what  part  of  the  area  of  the  continent? 

7.  The    area  included   in    the   three  temperate 
zones  equals  what  part  of  the  area  of  the  continent? 

8.  The    average  width  of   the  temperate    zone 
equals  what   part  of  the  length  of  the  continent? 

9.  The  average    width  of   the  warm  temperate 
zone  equals  what  part  of  the  average  width  of  the 
three  temperate  zones? 

10.  The  average  width  of   the  cold  temperate 
zone  equals  what  part  of  the  average  width  of  the 
three  temperate  zones? 

11.  The    average    width   of    the   tropical    zone 
equals    what    part   of  the    average    width   of    the 


190  NUMBER  WORK.  [November 

temperate  zones?  The  warm  temperate?    The  cold 
temperate  ? 

12.  The  average  width  of  the  Arctic  zone  equals 
what  part  of  the  length  of  the  continent? 

13.  The  average  width  of  the  north   polar  zone 
equals  what  part  of  the  width  of  the  tropical  zone? 

14.  The  average  width  of  the  Arctic  zone  equals 
what  part  of  the  average  width  of  the  tropical  zone  ? 

15.  The  area  of  the  continent  lying  south  of  the 
mean  annual  isotherm   of    60°  Fahr.   equals  what 
part  of  the  area  of  the  entire  continent?     Lying 
north  ? 

16.  The  area  lying  south  of  the  mean  annual 
isotherm  of  60°  Fahr.  equals  what  part  of  the  area 
lying  north  of  it? 

17.  The  area  lying  south  of  the  mean  annual 
isotherm  of  50°  equals  what  part  of  the  area  of  the 
entire  continent? 

18.  The    area    included     between    the    mean 
annual  isotherms   60°  and  70°  Fahr.,  equals  what 
part  of  the    area  between    the    mean  annual  iso- 
therms 70°  and  80°  Fahr.  ? 

19.  The  area  lying  south  of  the   mean   annual 
isotherm  70°  Fahr.  equals  what  part  of  the  area 
of  the  continent? 

20.  The  area   lying  south  of  the  mean  annual 
isotherm  40°  Fahr.  equals  what  part  of  the  area 
of  the  continent? 

21.  The   area  lying    south    of   the   July    mean 
isotherm  of  60°  Fahr.  equals  what  part  of  the  area 
of  the  continent? 

22.  The  area  lying  south  of  the  January  mean 


November]  GEOGRAPHY.  191 

isotherm   of   00°    Fahr.  equals   what   part   of    the 
area  of  the  continent? 

23.  The  area  between  the  July   mean  isotherm 
of  60°  Fahr.  and  January  mean  isotherm  of  60° 
Fahr.  equals  what  part  of  the  continent? 

B.  Rainfall. 

24.  The  average  annual  depth  of  rainfall  in  the 
Gulf  region  equals  what   part  of   the  average  on 
the  Atlantic  slope? 

25.  The  average  annual  depth  of  rainfall  south 
of  the   Potomac  equals  what  part  of  the  average 
north  of  it,  within  the  United  States  ? 

26.  The  mean   annual  depth  of  rainfall  in  the 
Ohio  basin  equals  what  part  of  the  average  in  the 
Missouri  basin? 

27.  The  mean  annual  depth  of  rainfall  in  the 
Ohio  basin  equals  what  part  of  the  average  in  the 
Gulf  region? 

28.  The  mean  annual  depth  of  rainfall  of  the 
region  west  of  the  Mississippi,  south  of  the  36th 
parallel,  equals  what  part  of  the   average  in  the 
same  latitude  east  of  the  Mississippi  ? 

29.  The   mean   annual  depth  of  rainfall  of  the 
eastern  highland  equals  what  part  of  the  average 
of  the  western  highland  ? 

30.  The  mean  annual  depth  of  rainfall  between 
the  Rocky  Mountains  and  the  Mississippi  River 
equals  what  part  of  the  average  between  the  Mis- 
sissippi River  and  the  Alleghany  Mountains? 

31.  The  mean  annual  depth  of  rainfall  north  of 
the   Great  Lakes  equals  what  part  of  the  average 
south  of  them  ? 


192  NUMBER  WORK.  [November 

III.     RATIO. 
A.    Zones. 

1.  What  is  the  ratio  of  the  area  included  in  the 
tropical  zone  to  the  area  of   the  entire  continent? 

2.  What  is  the  ratio  of  the  area  included  in  the 
warm    temperate  zone  to   the  area  of    the  entire 
continent  ? 

3.  What  is  the  ratio  of  the  area  included  in  the 
temperate  zone  to  the  area  of  the  entire  continent  ? 

4.  What  is  the  ratio  of  the  area  included  in  the 
cold  temperate  zone  to  the  area  of  the  entire  con- 
tinent? 

5.  What  is  the  ratio  of  the  area  included  in  the 
Arctic  zone  to  the  area  of  the  entire  continent  ? 

6.  What  is  the  ratio  of  the  area  included  in  the 
north  polar  zone  to  the  area   of  the    entire  con- 
tinent? 

7.  What  is  the  ratio  of  the  area  included  in  the 
three  temperate  zones    to  the  area  of  the    entire 
continent  ? 

8.  What  is  the  ratio  of  the  average  width  of  the 
temperate  zone  to  the  length  of  the  continent? 

9.  What  is  the  ratio  of  the  average  width  of  the 
tropical  zone  to  the  length  of  the  continent  ? 

10.  What  is  the  ratio  of  the  average  width  of 
the  Arctic  zone  to  the  length  of  the  continent? 

11.  What  is  the  ratio  of  the  width  of  the  warm 
temperate  zone  to  the  length  of  the  continent? 

12.  What  is  the  ratio  of  the  average  width  of 
the  temperate  zone  to  the  length  of  the  continent  ? 

13.  What  is  the  ratio  of  the  average  width  of 
the  cold  temperate  zone  to  the  length  of  the  con- 
tinent? 


November]  GEOGRAPHY.  193 

14.  What  is  the  ratio  of  the  average  width  of 
the  north  polar  zone  to  the  length  of  the  continent? 

15.  What  is  the  ratio  of  the  area  lying  south  of 
the  mean  annual  isotherm  of  (30°  Fahr.  to  the  area 
of  the  entire  continent? 

16.  What  is  the  ratio  of  the  area  lying  north  of 
the  mean  annual  isotherm  of  60°  Fahr.  to  the  area 
of  the  entire  continent? 

17.  What  is  the  ratio  of  the  area  lying  south  of 
the  mean  annual  isotherm  (30°  Fahr.  to  the  area 
lying  north  of  the  same? 

18.  What  is  the  ratio  of  the  area  lying  south  of 
the  mean  annual  isotherm  of  60°  Fahr.  to  the  area 
lying  south  of  the  mean  annual  of  50°  Fahr.  ? 

19.  What  is  the  ratio  of  the  area  lying  south  of 
the  mean  annual  isotherm  of  50°  Fahr.  to  the  area 
of  the  entire  continent? 

20.  What  is  the  ratio  of  the  area  lying  south  of 
the  mean  annual  isotherm  of  40°  Fahr.  to  the  area 
of  the  entire  continent? 

21.  What  is  the  ratio  of  the  area  lying  south  of 
the  mean  annual  isotherm  of  50°  Fahr.  to  the  are-a 
lying  south  of  the   mean   annual  isotherm  of  40° 
Fahr.? 

22.  What  is  the  ratio  of  the  area  lying  south  of 
the   mean  isotherm  of  60°  Fahr.  in  July  to   that 
lying  north  of  it? 

23.  What  is  the  ratio  of  the  area  lying  south 
of  the  January  mean  isotherm  of  60°  Fahr.  to  that 
lying  north  of  it? 

24.  What  is  the  ratio  of  the  area  lying  south  of 
the  January  mean  isotherm  of  60°  Fahr.   to   that 
south  of  the  July  mean  of  60°  Fahr.? 


194  NUMBER  WORK.  [November 

B.     Rainfall. 

25.  What  is   the    ratio  of  the   average    annual 
depth  of  rainfall  in  the   Mississippi   basin  to  the 
average  on  the  Atlantic  slope? 

26.  What  is   the  ratio  of   the    average    annual 
depth  of   rainfall  in   the  Mississippi  basin  to  the 
average  on  the  Pacific  slope? 

27.  What  is  the  ratio  of  the  average  annual  depth 
of  rainfall   west  of  the   Mississippi   River  to   the 
average  east  of  it? 

28.  What  is  the    ratio   of  the    average    annual 
depth  of  rainfall  in  the   Mississippi  basin  to  the 
average  of  the  Gulf  region? 

29.  What  is  the  ratio  of  the  mean  annual  depth 
of  rainfall  in  the  St.  Lawrence  basin  to  the  average 
in  the  Ohio  basin? 

30.  What  is  the  ratio  of  the  mean  annual  depth 
of  rainfall  in  the  Ohio  basin  to  the  average  of  the 
Missouri  basin? 

31.  What  is  the  ratio  of  the  mean  annual  depth 
of   rainfall  south  of  the  mean  isotherm   60°  Fahr. 
to  that  north  of  it,  within  the  United  States  ? 

32.  What  is  the  ratio  of  the  mean  depth  of  rain- 
fall  in  the   United    States   during   winter  to  the 
average  during  the  summer? 

IV.     PERCENTAGE. 
A .     Zones. 

1.  The  area  included  in  the  tropical  zone  equals 
what  per  cent  of  the  area  of  the  continent? 

2.  The  area  included  in  the    warm    temperate 
zone  equals  what  per  cent  of  the  area  of  the   con- 
tinent? 


Xovembei-l  QEOGRAP&Y.  195 

;J.   The    area  included    in  the    temperate    zone 
equals  what  per  cent  of  the  area  of  the  continent? 

4.  The  area  included  in  the  cold  temperate  zone 
equals  what  per  cent  of  the  area  of  the  continent? 

5.  The  area  included  in  the  Arctic  zone  equals 
what  per  cent  of  the  area  "of  the  continent? 

6.  The  area  included  in   the  north  polar    zone 
equals  what  per  cent  of  the  area  of  the  continent  ? 

7.  The  area  included   in    the  three   temperate 
zones  equals  what  per  cent  of  the  area  of  the  con- 
tinent ? 

8.  The   average    width    of     the    tropical     zone 
equals  what  per   cent  of  the  length  of  the  conti- 
nent ? 

9.  The  average   width  of  the   warm  temperate 
zone  equals  what  per  cent  of  the  length  of  the  con- 
tinent ? 

10.  The  average   width   of  the  temperate  zone 
equals  what  per  cent   of  the  length   of  the  conti- 
nent ? 

11.  The  average  width    of  the  cold   temperate 
zone  equals  what  per  cent  of  the   length   of  the 
continent  ? 

12.  The    average    width    of  the     Arctic    zone 
equals  what  per  cent  of  the  length   of   the  conti- 
nent ? 

13.  The  average  width  of  the -north  polar    zone 
equals  what  per  cent  of  the   length  of  the  conti- 
nent? 

14.  The  average  width  of  the  three  temperate 
zones  equals  what  per  cent  of   the  length   of  the 
continent  ? 


6  NUMBER  WORK.  [November 

15.  The  area  lying  south   of   the   mean  annual 
isotherm  of  60°  Fahr.  equals  what  per  cent  of  the 
area  of  the  continent? 

16.  The  area  lying  south  of  the   mean  annual 
isotherm  of  60°  Fahr.  equals  what  per  cent  of  the 
area  north  of  it? 

17.  The  area  lying  south  of  the   mean  annual 
isotherm  of  60°  Fahr.  equals  what  per  cent  of  the 
area  lying  south  of  the  mean  annual  isotherm  50' 
Fahr.  ? 

18.  The  area  lying  south  of  the  mean  annual 
isotherm  of  50°  Fahr.  equals  what  per  cent  of  the 
area  lying  south  of  the  mean  annual  isotherm  40° 
Fahr.? 

1$.  The  area  lying  south  of  the  mean  annual 
isotherm  of  50°  degrees  Fahr.  equals  what  per 
cent  of  the  area  of  the  continent  ? 

20.  The   area  lying  south  of  the  mean  annual 
isotherm  of  40°  Fahr.  equals  what  per  cent  of  the 
area  of  the  continent  ? 

21.  The  area  lying  south  of  the  mean  July  iso- 
therm of   60°    Fahr.  equals  what   per  cent  of   the 
area  of  the  continent  ? 

22.  The  area  lying  south  of   the  mean  January 
isotherm  of  60°  Fahr.  equals  what  per  cent  of  the 
area  of  the  continent? 

23.  The  area  lying  south  of  the  mean  July  iso- 
therm of  60°  Fahr.  equals  what  per  cent  of  the 
area  of  the  continent? 

24.  The  area  lying  south  of  the  mean  January 
isotherm  of  5CP  Fahr.  equals  what  per  cent  of  the 
area  of  the  continent? 


November]  (iI-:<)GKAl>HY.  191 

25.  The  area  lying  south  of  the  mean  January 
isotherm  of  50°  Fahr.  equals  what  per  cent  of  the 
area  lying  south  of  the  mean  July  isotherm  of  50° 
Fahr.? 

B.    Rainfall. 

26.  The  mean   annual  depth  of  rainfall  on  the 
Atlantic  slope  equals  what  per  cent  of  the  average 
in  the  Mississippi  basin? 

27.  The  mean  annual  depth   of  rainfall  in  the 
Gulf  States  equals  what  per  cent  of  the  average  in 
the  Mississippi  basin? 

28.  The  mean  annual  depth  of  rainfall  on  the 
Pacific  slope  equals  what  per  cent  of  the  average 
in  the  Mississippi  basin  ? 

29.  The  mean  annual  depth  of  rainfall  west  of 
the  Mississippi  River  equals  what  per  cent  of  the 
average  east  of  it? 

30.  The  mean  annual  depth  of  rainfall  east  of 
the  Mississippi  River  and  north  of  the  Ohio  River 
equals  what  per  cent  of   that  south  of  the  Ohio 

.River? 

31.  The  mean  annual  depth  of  rainfall  in  the 
Missouri  basin  equals  what  per  cent  of  the  average 
of  the  Ohio  basin  ? 

32.  The  mean  annual  depth  of  rainfall  in  the  St. 
Lawrence  basin  equals  what  per  cent  of  the  average 
in  the  Ohio  basin  ? 

33.  The  mean  annual  depth  of  rainfall  in  the  St. 
Lawrence  basin  equals  what  per  <fent  of  the  aver- 
age in  the  Gulf  States? 

34.  The  mean  annual  depth  of  rainfall  in  the 


198 


NUMBER  WORK. 


[November 


St.   Lawrence  basin  equals  what   per   cent  of  the 
average  in  the  Missouri  basin? 

35.  The  mean  annual  depth  of  rainfall  in  the 
St.  Lawrence  basin  equals  what  per  cent  of  the 
average  on  the  Pacific  slope? 


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PARKER'S  HOW  TO  STUDY  GEOGRAPHY. 

Prepared  for  the  Professional  Training  Class  in  the  C 
County  Normal.  400  pages,  -  price,  8 

PARKER'S  TALKS  ON  TEACHING. 

This  is  a  Collection  of  notes  on  Teaching  as  given  by  Francis 
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PARKER'S  QUINCY  COURSE  IN  ARITHMETIC. 

A  pamphlet  giving  instructions  in  Teaching  Arithmetic 
Primary  grades,  ...  price,  S 

PARKER3S  HINTS  AND  SUGGESTIONS  ON  T 
TEACHING  OF  LANGUAGE. 

It  contains  actual  work  in  the  school-room—now  in  t 
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RICE3S  COURSE   OF   STUDY  IN   HISTORY  AND  L 
ERATURE. 

Miss  Rice  gives  a  very  valuable  talk  on  History  and  also 
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GIFFIN3S  HOW  NOT  TO  TEACH, 

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GRISWOLDJS    READING    AND    OBSERVATION    LE 
SON  CARDS. 

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JACKIY1AN3S  NATURE  STUDY. 

This  book  is  intended  to  furnish  a  guide  for  Teachers  in 
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NATURE  MYTHS  AND   STORIES  FOR    LITTLE  CH 
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By  FLORA.  J.  COOKE.  This  is  good  supplementary  readinc 
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EXERCISES  IN  ELOCUTION. 

By  F.  STUART  PARKER,  price,  3 

JACKMAN'S  SCIENCE  RECORD. 

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A.  FLANAGAN,  Chicago 


LD  21-100m-7,'33 


YC  03903 


